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Complex dynamic systems theory

Complex dynamic systems theory (CDST) is a perspective within applied linguistics and complexity science that views language and language learning as complex, adaptive systems characterized by numerous interdependent components evolving nonlinearly over time, leading to emergent patterns, self-organization, and variability arising from interactions among learners, contexts, and linguistic elements.^[1] Proposed in the 1990s by Diane Larsen-Freeman as an alternative to linear models, CDST emphasizes nonlinearity, where small changes in input or context can yield disproportionate effects on language development, and dynamical evolution driven by feedback loops and sensitivity to initial conditions.^[2] Unlike traditional views of language acquisition as predictable and linear, CDST highlights properties like chaos—deterministic yet sensitive trajectories—and criticality, enabling systems to operate at the edge of stability for enhanced adaptability in multilingual environments.^[3] Key principles include emergence, where higher-level language abilities arise from micro-level interactions without centralized control, as observed in conversational patterns or learner motivation dynamics.^[4] Self-organization guides systems toward stable states or attractors, such as proficiency plateaus, while scale-free dynamics manifest in fractal-like variability across utterance lengths or skill development timelines.^[5] Hierarchy and collective dynamics underscore multilevel adaptations in language use, far from equilibrium, fostering resilience amid fluctuating social and cognitive influences.^[2] These principles, informed by broader complexity science, employ tools like longitudinal data analysis and computational simulations to model language evolution.^[1] CDST has transformed understandings of second and multilingual language acquisition, assessment, and development by highlighting interconnectedness and temporal variability, challenging reductionist approaches and promoting holistic, process-oriented perspectives in linguistics and education.^[4]

Foundations

Terminology

Complex dynamic systems theory (CDST) represents a synthesis of complexity theory, which examines emergent patterns in interconnected systems, and dynamical systems theory, which models time-dependent changes in system states, applied to the study of language development in applied linguistics. This framework views language as a self-organizing system influenced by multiple interacting variables, such as input, interaction, and individual learner factors, leading to nonlinear trajectories in acquisition.^[6] The term CDST was recommended by Kees de Bot to unify these foundational theories in the context of second language acquisition (SLA).^[6] Alternative nomenclature includes "dynamic systems theory" (DST), often used interchangeably with CDST to emphasize temporal variability in language processes. Other variants are "chaos/complexity theory in SLA," highlighting unpredictable yet patterned outcomes akin to chaotic systems, as introduced in early applications to language learning. "Dynamic usage-based theory," as developed by Marjolijn Verspoor et al. (2012), integrates usage-based principles of frequency-driven learning with dynamic evolution over time.^[7] Additionally, the "Dynamic Model of Multilingualism" by Philip Herdina and Ulrike Jessner frames multilingual proficiency as a fluctuating system of language subsystems with interdependent activation levels. CDST is distinct from related fields such as connectionism, which simulates language acquisition via parallel neural network models focused on weighted connections and pattern recognition, without emphasizing systemic emergence. In contrast to usage-based linguistics, which posits grammar as an outcome of statistical patterns in linguistic input and usage (as in Michael Tomasello's construction grammar), CDST incorporates ongoing variability and attractor states across developmental timescales. The competition model, developed by Brian MacWhinney, models language processing through cue-strength competitions in comprehension and production, differing from CDST by prioritizing modular cue integration over holistic system dynamics. Etymologically, "complexity" traces to mid-20th-century mathematics and cybernetics, describing systems with non-decomposable interactions and emergent properties, as articulated by Warren Weaver in distinguishing simple, complicated, and complex phenomena. "Dynamic," rooted in 19th-century physics, refers to forces causing motion or change, evolving into dynamical systems theory through Henri Poincaré's analysis of nonlinear differential equations in celestial mechanics. These origins underscore CDST's interdisciplinary vocabulary for modeling language as an adaptive, evolving entity.

Origins

Complex dynamic systems theory (CDST) traces its origins to foundational work in applied mathematics and physics during the mid-20th century, particularly through the development of non-equilibrium thermodynamics. Ilya Prigogine, a Belgian physical chemist, introduced the concept of dissipative structures in the 1970s, describing how open systems far from equilibrium can self-organize into ordered patterns through energy and matter flows, challenging classical thermodynamics' focus on equilibrium states.^[8] Collaborating with philosopher Isabelle Stengers, Prigogine expanded these ideas in their seminal 1984 book Order Out of Chaos, which popularized dissipative structures as a framework for understanding complexity in natural systems, laying the mathematical groundwork for later applications beyond physics. The theory's transition into social sciences occurred in the 1980s, notably through psychologist Esther Thelen's research on infant motor development. Thelen applied dynamic systems principles to demonstrate that motor skills, such as crawling and walking, emerge from the nonlinear interactions of multiple subsystems—including neural, muscular, and environmental factors—rather than maturational stages alone.^[9] Her empirical studies, including those on the "disappearance and reappearance" of stepping reflexes in infants, illustrated how variability and self-organization drive developmental change, influencing fields like developmental psychology and cognitive science. This adaptation highlighted CDST's potential for modeling human behavior as emergent from contextual interactions, bridging physical sciences with behavioral domains. CDST entered linguistics and second language acquisition (SLA) in the late 1990s, catalyzed by Diane Larsen-Freeman's influential 1997 paper, which drew parallels between chaos/complexity science and language learning processes.^[10] Larsen-Freeman argued that language development exhibits dynamic traits like nonlinearity and sensitivity to initial conditions, shifting SLA research from linear models to complexity perspectives. This marked a pivotal adaptation, emphasizing language as a complex, adaptive system influenced by social and cognitive variables. Building on this, early key publications further solidified CDST in linguistics; for instance, de Bot, Lowie, and Verspoor's 2007 review in the Annual Review of Applied Linguistics framed SLA as a dynamic multilingual system with interacting variables over time. Similarly, Herdina and Jessner's 2002 Dynamic Model of Multilingualism proposed a psycholinguistic framework where multiple languages evolve through interdependent, time-sensitive changes, accounting for phenomena like language attrition and proficiency shifts in multilingual speakers. More recent syntheses, such as Zhao et al.'s 2021 scoping review of 25 years of CDST research in language learning, highlight its growing empirical foundation and methodological advancements.^[11]

Definition

Complex dynamic systems theory (CDST) defines language as a complex adaptive system that is dynamic, nonlinear, and emergent, consisting of interdependent subsystems—such as phonology, syntax, semantics, and pragmatics—that interact and evolve over time in response to environmental inputs and internal feedback loops.^[1]^[12] This perspective treats language not as a static structure but as a holistic entity where changes in one subsystem can propagate unpredictably across the entire system, leading to patterns of variability and stability.^[13] As a metatheory, CDST provides an ontological framework for understanding language development as a self-organizing process, where acquisition emerges from the ongoing adaptation of interconnected components rather than following a predetermined, linear trajectory.^[11] This contrasts sharply with traditional second language acquisition (SLA) theories, such as input-output models, which posit development as a sequential accumulation of linguistic knowledge driven primarily by external exposure and practice.^[12] In CDST, variability is inherent and informative, reflecting the system's sensitivity to contextual and individual factors rather than error or deviation from a norm.^[1] A key application within CDST is the Dynamic Model of Multilingualism (DMM), which incorporates language attrition as an integral dynamic alongside acquisition, positing that multilingual systems require continuous effort for maintenance to counteract natural decay and promote growth across languages. This model highlights how general language proficiency—encompassing metalinguistic awareness and cross-linguistic interactions—serves as a stabilizing factor in the evolving multilingual repertoire.

Core Concepts

Main Characteristics

Complex dynamic systems are defined by several empirical properties that distinguish them from simpler linear or isolated systems. These characteristics arise from the interplay of multiple components evolving over time, often leading to unpredictable yet patterned behaviors. Nonlinearity is a core feature, where system outputs are not proportional to inputs, allowing small initial changes to amplify into significant outcomes—a phenomenon known as the butterfly effect. This sensitivity was first demonstrated in Edward Lorenz's 1963 model of atmospheric convection, where minute alterations in initial conditions produced vastly different long-term trajectories in a deterministic system. Interconnectedness manifests through bidirectional influences among components, forming feedback loops that propagate changes across the system. Positive feedback amplifies deviations, while negative feedback stabilizes dynamics, creating a web of dependencies that precludes isolated analysis. This property is essential for complexity, as direct interactions between elements' states enable emergent behaviors beyond individual contributions.^[14] Self-organization occurs when ordered patterns emerge spontaneously from local interactions without centralized control, often in far-from-equilibrium conditions. Ilya Prigogine's work on dissipative structures illustrates this, showing how systems dissipate energy to maintain structure, leading to phase transitions and novel configurations through internal fluctuations. Complex dynamic systems are typically open, engaging in continuous exchange of matter, energy, or information with their surroundings, which drives evolution and prevents stasis. This openness fosters adaptability, allowing the system to co-evolve with its environment by reorganizing in response to perturbations, thereby enhancing resilience and robustness over time.^[14] Finally, variability is intrinsic to these systems, representing structured fluctuations that reflect underlying dynamics rather than random error. Such intra-system variations enable exploration of state space and adaptation, as seen in the non-random patterns of deviation in chaotic attractors.^[15]

Key Principles in Language Systems

In complex dynamic systems theory (CDST), emergence refers to the way language proficiency develops nonlinearly from the interactions among subsystems, such as vocabulary, grammar, and pragmatics, rather than through isolated, linear acquisition of components. For instance, vocabulary expansion and grammatical structures co-evolve through repeated use in communicative contexts, giving rise to higher-level abilities like fluent discourse without a predetermined blueprint. This emergent property underscores how language as a system self-organizes, producing novel patterns that are greater than the sum of its parts, as seen in second language learners' gradual integration of lexical items into syntactic frames.^[11] A defining feature of language systems under CDST is the presence of multiple interacting timescales, spanning from rapid micro-level variations to long-term macro-level changes. Phonetic variations in speech production can occur on millisecond scales during real-time interactions, while broader shifts, such as long-term language attrition in bilinguals, unfold over years due to reduced exposure. These nested timescales illustrate how short-term fluctuations, like momentary hesitations in word retrieval, influence and are influenced by extended developmental trajectories, creating a dynamic interplay that drives overall proficiency. Language use in CDST is characterized by attractors—stable states toward which the system gravitates—and the potential for shifts triggered by perturbations. In linguistic contexts, attractors manifest as preferred patterns, such as a learner's consistent reliance on certain syntactic constructions during early stages of acquisition, providing temporary stability amid variability.^[11] However, external or internal perturbations, like immersion in a new linguistic environment or cognitive stress, can destabilize these attractors, leading to phase transitions where the system reorganizes into new stable configurations, such as enhanced fluency.^[2] Soft-assembly describes how language structures form temporarily and flexibly in response to immediate task demands, rather than relying on fixed, pre-existing modules. For example, during spontaneous conversation, speakers assemble ad-hoc grammatical patterns by co-adapting lexical choices and discourse rules on the fly, dissolving once the interaction ends.^[16] This principle highlights the transient nature of linguistic organization, where subsystems like phonology and semantics align situationally without rigid hierarchies.^[11] Context plays a pivotal role in shaping the behavior of language systems in CDST, integrating social, cognitive, and environmental factors that continuously influence system dynamics. Social interactions, such as peer feedback in multilingual settings, can amplify variability and promote adaptation, while cognitive elements like attention modulate how subsystems interact. These contextual influences ensure that language emerges relationally, with no isolated components, as the system responds to ongoing perturbations from its surroundings.^[11] Nonlinearity and feedback loops, as general properties of complex systems, further underpin these principles by enabling amplified effects from small changes in language use.

Applications in Language Learning

Motivation in Second and Third Language Acquisition

In complex dynamic systems theory (CDST), motivation in second and third language acquisition is conceptualized as a complex subsystem that dynamically interacts with cognition, emotion, and environmental factors, rather than a static trait.^[17] This perspective integrates Dörnyei's L2 Motivational Self System, which emphasizes idealized future selves and ought-to selves, by viewing these motivational components as emergent properties within a nonlinear network of influences, such as learner agency and social context. For instance, emotional states like anxiety or enjoyment can amplify or dampen motivational trajectories through bidirectional feedback with cognitive processes, leading to self-reinforcing cycles that shape language learning persistence.^[17] Motivation exhibits non-linear fluctuations over time in CDST, characterized by peaks and troughs driven by feedback loops, where initial successes or setbacks can create attractor states that propel or hinder progress.^[18] Unlike linear models that assume steady progression, this dynamic view posits that motivation evolves through phase transitions, influenced by contextual perturbations such as instructional feedback or peer interactions, resulting in unpredictable yet patterned variability. For example, a temporary motivational boost from perceived competence may reinforce effort via positive loops, but external stressors could trigger downturns, highlighting motivation's sensitivity to ongoing system interactions.^[18] In second language (L2) acquisition, CDST frames motivation as responsive to primary language contrasts, but third language (L3) learning introduces enhanced complexity due to cross-linguistic synergies and interdependencies among multiple languages.^[19] Positive transfer from L1 and L2 acts as an attractor, facilitating motivational stability through perceived interconnections, such as shared linguistic features that boost confidence in L3 tasks.^[20] This added layer of complexity in L3 contexts often results in more volatile motivational dynamics, as learners navigate competing language systems and identities.^[21] Empirical evidence from longitudinal studies underscores motivation's sensitivity to initial conditions, such as learner identity, in both L2 and L3 settings. Similarly, research on five university L3 learners in China documented how initial multilingual identities influenced motivational peaks, with cross-language synergies creating stable attractors amid variability over 18 months.^[22] These findings illustrate CDST's emphasis on individuality, where small initial differences in self-perception can yield divergent long-term outcomes in language motivation.

Language Assessment and Variability

In complex dynamic systems theory (CDST), language assessment diverges sharply from traditional paradigms that rely on static, standardized tests designed to yield fixed proficiency scores, often modeled after native-speaker norms and assuming linear progression. These conventional approaches overlook the inherent fluctuations and context-dependent nature of language use, treating variability as error or noise rather than a signal of adaptive development. In contrast, CDST posits that language proficiency emerges dynamically through interactions among subsystems such as cognition, emotion, and environment, necessitating assessments that are sensitive to contextual variations and individual trajectories. For instance, Ahmar Mahboob and Lydia Dutcher's dynamic approach to language proficiency emphasizes adaptability to diverse communicative settings, challenging the reduction of proficiency to singular metrics and advocating for evaluations that capture how learners negotiate meaning in real-time interactions.^[23] CDST reframes proficiency not as a static endpoint but as a fluctuating range, where learners exhibit profiles of strengths and weaknesses that evolve nonlinearly over time, influenced by self-organization processes in which subsystems adapt and stabilize through variability. This perspective highlights intra-individual variability—such as temporary regressions or sudden advances—as essential for growth, rather than deviations from a norm. Longitudinal studies, for example, reveal that oral production in second language learners shows patterned fluctuations, with increased variability often preceding developmental leaps, allowing for the construction of personalized proficiency profiles that track these dynamics across contexts. By incorporating such variability, assessments can better reflect the emergent nature of language systems, prioritizing holistic patterns over isolated scores.^[24] Practical applications of CDST in language assessment include portfolio-based methods, which compile longitudinal artifacts like writing samples or recordings to illustrate developmental ranges and contextual adaptations, and adaptations of dynamic indicators originally developed for early literacy skills, such as those measuring fluency and comprehension in real-time tasks tailored to multilingual learners. These tools enable educators to monitor non-linear progress without oversimplifying complexity, fostering context-sensitive feedback that supports self-organization in learning. Recent work as of 2024 has further applied CDST to process-oriented assessments, emphasizing ongoing variability in second language development to inform more adaptive evaluation frameworks.^[25] However, implementing CDST-informed assessments poses challenges, including the difficulty of quantifying non-linear trajectories amid high variability, the need for dense data collection to avoid ergodic assumptions that generalize across individuals, and the risk of reducing dynamic processes to simplistic metrics if analytical methods fail to preserve systemic interconnections.^[25]

Multilingualism and Language Development

Complex dynamic systems theory (CDST) applied to multilingualism emphasizes the interplay of multiple language systems as interdependent components within a holistic, adaptive framework. The Dynamic Model of Multilingualism (DMM), developed by Herdina and Jessner in 2002, portrays the multilingual speaker's linguistic repertoire as a dynamic ecosystem where languages evolve through ongoing interactions influenced by usage, exposure, and cognitive factors. In this model, each language functions with specific activation thresholds that determine its readiness for use, allowing for fluid shifts in proficiency levels across the system rather than isolated development.^[26]^[27] Language development in multilingual contexts follows non-linear trajectories characterized by phases of stability interspersed with rapid changes, reflecting the self-organizing nature of complex systems. These paths exhibit variability as a sign of growth, where periods of apparent stagnation may precede breakthroughs, such as during heightened exposure to a new language. Critical periods, traditionally viewed as fixed windows for acquisition, are reinterpreted in CDST as potential phase shifts—moments of increased system sensitivity leading to structural reorganization in proficiency. For instance, longitudinal studies of bilingual children acquiring a third language show irregular progress in syntax and vocabulary, with sudden advancements tied to contextual triggers like immersion.^[1]^[28] Cross-linguistic influence in multilingual development emerges as a key property of these interconnected systems, manifesting as positive or negative transfer that shapes L3 acquisition outcomes. In L3 learning, prior languages (L1 and L2) do not exert static effects but dynamically interact, with transfer arising from factors like typological proximity and recency of use; for example, German-English bilinguals acquiring French as L3 may draw positive phonological transfer from English due to shared features, while negative interference from German affects gender agreement. This bidirectional influence, including reverse transfer from L3 to L1/L2, highlights emergent patterns unique to the individual's multilingual profile rather than predictable hierarchies.^[19]^[29] Recent advancements integrate CDST with dynamic usage-based (DUB) perspectives, offering a holistic lens on bi- and multilingualism that prioritizes usage patterns in driving system evolution. Verspoor's DUB approach, evolving through the 2020s, underscores how frequent, meaningful interactions across languages foster adaptive growth, as seen in studies of multilingual learners where motivational and usage dynamics co-evolve to enhance overall proficiency.^[30]^[31] As of 2025, further syntheses of CDST have explored its role in empowering language teachers through understanding dynamic motivational and developmental processes in multilingual contexts.^[32] This framework extends DMM by incorporating variability in usage as a catalyst for long-term multilingual competence, emphasizing individualized trajectories over universal stages.

Methods and Techniques

Data Collection Approaches

In complex dynamic systems theory (CDST) applied to language systems, data collection approaches emphasize capturing the nonlinear, variable, and interactive nature of language development over time, necessitating methods that track fluctuations at individual and subsystem levels.^[33] Longitudinal designs are prioritized to reveal emergent patterns, as static snapshots fail to account for the dynamic interplay of factors like motivation, proficiency, and context in second language acquisition (SLA).^[34] Time-series data collection involves repeated measures over extended periods to monitor variability and trajectories in language subsystems, such as lexicon, syntax, or fluency. For instance, in SLA studies, researchers often gather weekly proficiency logs or self-assessments of speaking automaticity on scales from 0 to 100, allowing visualization of fluctuations and non-linear progress over months or years.^[35] This approach, rooted in dynamic systems principles, treats intra-individual variability as a signal of development rather than error, as demonstrated in longitudinal tracking of syntactic complexity in writing samples collected biweekly over a semester.^[33] Seminal work by Verspoor et al. (2011) highlights how such dense time-series data from one learner's writing over three years uncovers regressive phases alongside advancement, illustrating subsystem interactions. Case studies and idiographic approaches focus on in-depth tracking of individual learners to uncover unique developmental trajectories, emphasizing particularization over generalization in CDST research. Multiple-case designs, such as those examining three plurilingual participants' language repertoires through retrodictive qualitative modeling, reveal personalized patterns of subsystem coupling, like how prior languages influence target language automaticity.^[35] These methods prioritize intra-learner variability, as seen in studies of Finnish learners where repeated accuracy and complexity measures across sessions highlight divergent paths not visible in group averages. Larsen-Freeman (2017) underscores the value of such idiographic investigations for theory-building, using individual cases to model dynamic change processes in SLA. Multimodal data collection integrates diverse sources—oral, written, and interactional—to capture interactions across language subsystems, providing a holistic view of dynamic phenomena. Researchers combine quantitative metrics, like complexity-accuracy-fluency (CAF) indices from speech samples, with qualitative data such as open-ended interviews and questionnaires, enabling analysis of how oral production influences written output over time.^[33] For example, biweekly interviews allowing code-switching alongside weekly surveys of lexical use track co-adaptive patterns in plurilingual contexts, revealing subsystem dependencies.^[35] This approach aligns with CDST's emphasis on interconnectedness, as in studies merging journaling with feedback sessions to document variability in EFL learners' development.^[36]

Analytical Methods

Analytical methods in complex dynamic systems theory (CDST) applied to language systems emphasize the examination of time-series data to capture variability, non-linearity, and emergent patterns in language development and use. These tools address the inherent complexity of dynamic processes by focusing on longitudinal trajectories rather than static snapshots, enabling researchers to model interactions among subsystems such as proficiency levels, learner agency, and contextual influences. Unlike traditional linear statistical approaches, CDST analytical methods prioritize techniques that reveal state transitions, coordination, and attractor dynamics in language learning. Min-max graphs and density plots serve as foundational visualization tools for illustrating the range and distribution of variability in language measures, such as lexical diversity or syntactic complexity over time. Min-max graphs plot the upper and lower bounds of measures across developmental phases, highlighting periods of expansion or stabilization in a learner's linguistic system, while density plots overlay kernel estimates to show the probability distribution of values, revealing multimodal patterns indicative of subsystem interactions. These methods, introduced in early CDST applications to second language development, facilitate the identification of non-linear growth trajectories without assuming normality in data distribution. For instance, in analyzing L2 writing samples, min-max graphs can depict fluctuating complexity ranges that correlate with task demands, underscoring the adaptive nature of language systems.^[37] Hidden Markov models (HMMs) provide a probabilistic framework for modeling unobserved state transitions in language proficiency, treating development as a sequence of latent states influenced by hidden variables like motivation or exposure. In HMMs, observed data—such as utterance lengths or error rates—are emissions from underlying Markov chains, allowing detection of shifts from novice to intermediate states through Viterbi algorithms that infer the most likely state sequence. Applied to longitudinal speaking and writing data from identical twins, HMMs revealed distinct developmental paths, with speaking showing rapid state reorganizations compared to writing's gradual stabilization. Extensions in recent CDST reviews integrate HMMs with agent-based simulations to account for interpersonal dynamics, enhancing their utility for predicting proficiency plateaus in multilingual contexts. Spearman's rank correlation coefficient is employed to detect monotonic non-linear relationships in time-series language data, where traditional Pearson correlations may fail due to non-normal distributions or ordinal scales common in linguistic metrics. By ranking variables and computing the correlation of ranks, Spearman's rho (ρ) quantifies the strength and direction of associations, such as between variability in vocabulary use and overall proficiency gains over time, with values ranging from -1 to 1. In CDST analyses of second language variability, this method has identified non-linear dependencies, for example, showing that increased fluctuation in morphosyntactic measures precedes attractor formation in advanced learners, without assuming linearity. Cross-recurrence quantification analysis (CRQA) quantifies patterns of coordination and recurrence in bivariate time series from learner interactions, capturing how interpersonal synchrony emerges in language use. CRQA generates a cross-recurrence plot visualizing repeated states between two series—such as turn-taking in dialogues—and derives metrics like recurrence rate (percentage of recurring points) and determinism (proportion of diagonal lines indicating predictability). In studies of dyadic second language tasks, CRQA has demonstrated heightened coordination during collaborative problem-solving, with longer diagonal lines signaling stable entrainment in fluency measures between learners. This approach reveals emergent social dynamics, such as mutual adaptation in pronunciation or lexical alignment, central to CDST views of language as a co-constructed system.

Critical Perspectives

Criticisms and Limitations

One major criticism of complex dynamic systems theory (CDST) in second language acquisition (SLA) concerns its idiographic focus, which prioritizes detailed, individual-level analyses over nomothetic generalizations applicable across learners. This approach, while rich in capturing unique developmental trajectories, is argued to limit the theory's ability to yield universal predictions or scalable insights for broader educational practices. The absence of linear causality in CDST further complicates its empirical validation, as the framework rejects traditional cause-effect models in favor of emergent, nonlinear interactions among system components. Critics contend that this makes claims difficult to falsify, as outcomes cannot be reliably attributed to specific variables without the structured predictability of linear paradigms, potentially undermining the theory's scientific rigor. Methodological challenges also arise from the inherent complexity of CDST data analysis, which often involves longitudinal, multifaceted datasets prone to interpretive subjectivity. For instance, researchers may over-rely on visual representations such as state space grids or trajectory plots to illustrate dynamics, risking subjective interpretations that prioritize narrative coherence over objective metrics, thus hindering replicability. More recent critiques highlight CDST's under-engagement with quantitative rigor, where studies frequently lack advanced statistical tools to model nonlinearity, leading to calls for methods like generalized additive mixed models to enhance validity.^[38] Early criticisms, such as those by Kevin Gregg, questioned the metaphorical application of chaos/complexity concepts to SLA, arguing for more rigorous empirical testing over loose analogies.^[39] In response, proponents defend CDST's emphasis on descriptive power, arguing that its strength lies in illuminating contextual variability and system interactions rather than pursuing predictive universality, which may be unattainable in inherently open, adaptive language systems. This perspective positions CDST as complementary to traditional approaches, capable of supporting causal inferences and generalizability when integrated with rigorous analytical methods, as detailed in sections on analytical techniques.^[40]

Notable Researchers and Contributions

Diane Larsen-Freeman is widely recognized as a foundational figure in applying complex dynamic systems theory (CDST) to second language acquisition (SLA), with her seminal 1997 article introducing chaos/complexity science to reframe enduring SLA questions through the lens of nonlinear dynamics and emergent patterns.^[10] Her work emphasized how language learning involves self-organizing systems where variability and adaptation lead to stability, challenging linear models of progression. In more recent contributions, such as a 2022 webinar, Larsen-Freeman explored emergence in CDST, highlighting how novel language structures arise from interactions in dynamic contexts without predefined blueprints.^[3] Kees de Bot played a pivotal role in formalizing CDST's application to SLA, co-authoring influential early works that positioned language as a dynamic, interacting system evolving over time, including a 2007 paper that outlined a dynamic systems theory approach to acquisition processes. His contributions extended to multilingualism models, where he modeled language repertoires as adaptive systems influenced by aging and context, as seen in his 2020 overview of multilingualism and ageing that integrated CDST principles to explain shifting linguistic competencies.^[41] De Bot's framework underscored how multilingual systems exhibit greater complexity and non-linearity compared to monolingual ones, informing studies on language attrition and maintenance. Marjolijn Verspoor advanced CDST through her development of dynamic usage-based theory, which views language development as an emergent process shaped by usage patterns and variability, detailed in her 2014 co-authored work linking DST to usage-based approaches in SLA.^[42] From 2015 onward, she pioneered variability visualization tools, such as time-series analyses and density plots, to illustrate intra-learner fluctuations in linguistic features like complexity and accuracy, enabling researchers to track developmental trajectories without assuming fixed stages.^[43] These methods, applied in studies of L2 writing and Finnish acquisition, revealed how variability signals growth phases in usage-based learning.^[44] Zoltán Dörnyei integrated CDST into motivation research by examining its dynamic nature within the L2 Motivational Self System, as explored in his 2014 study on motivational currents that demonstrated how individual motivation fluctuates through stable and transitional phases influenced by contextual interactions.^[18] This work shifted focus from static traits to emergent motivational dynamics, showing how self-guides evolve nonlinearly to sustain long-term language learning efforts. Sarah Mercer contributed to CDST by incorporating complexity perspectives into language learner psychology during the 2010s, notably in her 2011 analysis of self-concept as a multifaceted, dynamic system prone to continuity and change across learning contexts.^[45] Her research highlighted how psychological factors like agency and mindset interact emergently, informing holistic models of learner identity in multilingual environments.^[46] Ulrike Jessner extended CDST to third language (L3) dynamics, emphasizing the heightened complexity of multilingual systems in her 2012 overview, which framed L3 acquisition as an adaptive process involving metalinguistic awareness and cross-linguistic synergies.^[47] Her 2023 book further modeled TLA from a CDST lens, illustrating how prior languages create emergent properties that accelerate or complicate new acquisitions.^[48] Phil Hiver and Ali H. Al-Hoorie provided a comprehensive synthesis of CDST's evolution in their 2021 scoping review, analyzing 25 years of research to identify trends in methodological innovations and theoretical applications across SLA domains. Hiver's additional focus on teacher development applied CDST to professional growth, as in his 2015 exploration of teacher immunity as a dynamic system that adapts through contextual stressors and resilience-building interactions.^[49]

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https://books.google.com/books?id=KKM0zlLcagQC
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ADynamic Model of Multilingualism: Perspectives of Change in ...
Additionally, the Dynamic Model of Multilingualism (Herdina & Jessner, 2002) emphasizes the fluid and adaptive nature of language systems in multilingual ...
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[PDF] Complex Dynamic Systems Theory and Second Language ...
Jul 28, 2022 · The field of Applied Linguistics was first introduced to Complex Dynamic Systems. Theory by Larsen Freeman (1997), later followed by De Bot ...Missing: Kees 1996
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https://www.jbe-platform.com/content/journals/10.1075/dujal.19003.eib
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A dynamic usage-based analysis of L2 written complexity ...
A collection of studies within the DUB approach (e.g., Spoelman & Verspoor ... language acquisition (ISLA) setting, Verspoor et al. (2020) assessed written ...
[31]
[PDF] Australian Journal of Applied Linguistics Multilingual Practice ... - ERIC
Language Policy, 13(1), 21–40. Huang, T., Steinkrauss, R., & Verspoor, M. (2021). The emergence of the multilingual motivational system in Chinese learners ...
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(PDF) Complex dynamic systems theory as a foundation for process ...
Apr 29, 2024 · In the past decades, complex dynamic systems theory (CDST) has been used as an important framework for studying second language development.
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https://www.researchgate.net/publication/380172798_Complex_dynamic_systems_theory_as_a_foundation_for_process-oriented_research_on_second_language_development
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[PDF] Applying Complex Dynamic Systems Theory to Identify Dynamic ...
In other words, the components of dynamic systems are open but completely interdependent (de Bot & Larsen-Freeman, 2011). ... Ten 'lessons' from complex dynamic ...Missing: Kees 1996
[35]
https://teslcanadajournal.ca/index.php/tesl/article/download/1479/1317/2113
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A Dynamic Approach to Second Language Development
As a result of chaotic variation among and within variables, it is impossible to separate the trajectory of complex systems (Verspoor et al., 2011) ; thus, ...
[37]
[PDF] Attractor States in Second Language Development - ERIC
In sum, examining attractor states is essential to understanding the dynamics of complex dynamic systems. The ubiquity of attractor states in SLD points to the ...
[38]
Intrinsic versus extrinsic motivation in EFL: a mixed-methods ...
Abstract. Motivation is a key determinant of success in foreign language learning, yet its dynamics in Central Asian contexts remain underexplored.
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[PDF] Reconciling the Divides: A Dynamic Integrative Analysis of ... - ERIC
Understanding that development is non-linear and varies for different linguistic features or writing abilities in different learners is crucial. However, it ...
[40]
Complex dynamic systems theory: A webinar with Diane Larsen ...
Oct 26, 2022 · In short, CDST is a theory of change that sees language as a contextualized dynamic system that is continually being transformed through use.
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https://brill.com/display/book/9789004445802/BP000006.xml
[42]
Dynamic Systems Theory and a usage-based approach to Second ...
Request PDF | On Jan 1, 2014, Marjolijn Verspoor and others published Dynamic Systems Theory and a usage-based approach to Second Language Development ...Missing: visualization | Show results with:visualization
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A dynamic usage based perspective on L2 writing
A dynamic usage based perspective on L2 writing. Marjolijn Verspoor*, Monika S. Schmid, Xiaoyan Xu. *Corresponding author for this work. Research output ...Missing: theory visualization 2015<|separator|>
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Dynamic Usage-based Principles in the Development of L2 Finnish ...
Aug 4, 2020 · For progress to take place, it is necessary for the learner to try out and possibly even overuse certain linguistic features (Lowie and Verspoor ...
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Language learner self-concept: Complexity, continuity and change
This paper aims at contributing to a fuller understanding of the nature and potential dynamism of self-concept in the foreign language learning domain.
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[PDF] The Complexity of Learner Agency | Semantic Scholar
Understanding learner agency as a complex dynamic system · Sarah Mercer. Linguistics, Education ; Agency in the classroom · L. V. Lier. Linguistics, Education.
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Complexity in Multilingual Systems - Jessner - Major Reference Works
Nov 5, 2012 · The investigation of the complexity of multilingualism, a phenomenon which seems to lend itself to being approached from a dynamic systems ...
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Third Language Acquisition from a Complexity Dynamic Systems ...
Bilingualism and multilingualism, meanwhile, are both complex phenomena, but what distinguishes them has primarily to be seen in the higher degree of complexity ...
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https://www.degruyterbrill.com/document/doi/10.21832/9781783092574-017/html