Dynamical Systems Theory Research Articles

Directives in Academia and Media During the Uncertainty

ABSTRACTThis study employs a discourse dynamic approach to analyze the directives used in academic and media corpora related to the pandemic. Underpinned by the Complex Dynamic Systems Theory, the discourse dynamic approach is used to examine the variation of linguistic features in the specified timescale. The analysis first presents the response of academia and media in reporting on Covid‐19 from a register perspective. Then the developmental trajectory reveals a nonlinear pattern of directives during the examined period in both corpora, presenting an evolving pattern of directives construction. We also notice dynamic interaction between directives and reported conditions, providing strong evidence of a complex system behind the linguistic phenomenon. This study sheds light on the distinctive practices adopted by the two communities when responding to the same event. The study demonstrates the feasibility of the integration of the corpus approach and the discourse dynamic approach and underscores evidence for the existence of a dynamic and complex system behind discursive construction.

Move to learn: considerations for providing upright, hands-free, self-initiated mobility to children with severe physical and communication disabilities

Development in children is sometimes described as a series of isolated milestones, e.g., first smile, first word, sitting, crawling, first step, and so on, even though that is not actually how human development unfolds. Rather, many of the skills that emerge during childhood are better understood using neuroplasticity, dynamic systems theory, and embodied cognition. Based on these findings and theories, we explore the potential impact that upright, hands-free, self-initiated mobility can have on children with severe physical and communication disabilities who use augmentative and alternative communication, specifically focusing on their growth in communicative competence. We discuss research that demonstrates the benefits to children with different physical abilities when they engage in upright, hands-free, self-initiated mobility. This article reflects the World Health Organization’s International Classification of Functioning, Disability and Health for Children and Youth by considering the importance of identifying functional communication needs and goals, taking into account participation barriers, communication limitations, and personal and environmental factors. We advocate for adopting family-centered, interprofessional collaborative service delivery models that more directly align with current theories of human development. Finally, we call for the adoption of implementation science to help bridge the existing gaps between theory and evidence-based practices.

The Influence of Students' Independent Use of Generative AI Tools on the EFL Writing Classroom: Recommendations for Students, Teachers, and Policymakers

This research explores the influence of generative AI tools on the EFL writing classroom through the lens of Complexity Dynamic Systems Theory (CDST), particularly with regard to the influence on classroom dynamics. The data were collected through semi-structured interviews with both teachers and students using an exploratory qualitative design. The results show that generative AI has disrupted writing classroom dynamics and resulted in a shift in assessment and classroom instructions. Also, since the rise of generative AI, noticeable changes have occurred in students’ writing. These tools have changed both the way they write and what they produce. The advent of generative AI has led to the emergence of new patterns changing the way that students engage with writing, changing teacher-student interactions, and ongoing feedback loops acting on steering classroom practices. These insights imply that the advent of generative AI has resulted in challenges and opportunities in EFL writing classrooms. These results highlight the adaptive nature of the writing classroom as a complex dynamic system, where stability and change coexist. The research concludes with recommendations for students, teachers, and policymakers on how to balance AI’s challenges and opportunities facing EFL writing classrooms.

Оценка степени управляемости и наблюдаемости объекта при синтезе робастных систем управления

Traditional criteria for assessing system properties allow us only to analyze qualitatively the controllability and observability of dynamic systems, which limits the possibility of predicting the success of the synthesis of control systems. Research shows that the established methodology to obtain and apply quantitative assessment of controllability and observability cannot be considered complete, and thus, the task of their improvement continues to be relevant. One of the least developed issues of the theory is the development and application of quantitative criteria to assess the system properties of objects for predicting and improving the robust properties of synthesized control systems. The paper uses methods of vector-matrix and structural representation of dynamic objects and systems in state coordinates and in input-output relations. Methods of calculating controllability and observability Grammians are applied, as well as their singular decompositions for the initial and canonical forms of object representation. Parametric synthesis of state controllers and input-output polynomial controllers is performed using modal and modal-polynomial control methods. Evaluation of the effectiveness of the obtained results is carried out using digital modeling methods. A method has been developed and matrix criteria have been obtained for quantitative assessment of the degree of controllability and observability of an object. They are based on comparison of the degree of closeness of its real structure to reference models in the form of canonical forms of controllability and observability, pre-coordinated by input and output with the real structure of the object. The proposed criteria to assess system properties are not only more convenient and informative for assessing and comparing system properties of control objects, but also useful when developing methods to improve them. In comparison with the traditional method of assessing the system properties of control objects based on the use of singular decompositions of controllability and observability grammians, the developed method and the criteria for assessing the degree of controllability and observability of minimum-phase SISO objects formed on its basis allow us to predict more accurately the robust properties of synthesized modal control systems with inertialess and dynamic controllers, to perform their structural optimization, and also to assess quantitatively the effectiveness of various methods to improve the indicated system properties.

Discrete perceptron based on probabilistic estimates of shifted synaptic signals

Purpose. Improvement of existing methods and development of new approaches for the digital processing of discrete signals in the field of artificial neural networks, as well as the formulation of principles for the structural implementation of discrete perceptrons. Methodology. The presented scientific results and conclusions were obtained using methods of statistical analysis and digital signal processing, probability theory and mathematical statistics, signal and system theory, as well as through computational experiments and modeling. Findings. The research showed the potential and prospects of using the proposed perceptron structure, which processes synaptic signals based on statistical estimation of their discrete states. The signal shifting is implemented through addition of weight coefficients, which allows avoiding multiplication operations and, as a result, reduces algorithmic and computational complexity. Furthermore, using a discrete basis allows accelerating the training process by reducing the possible range of signal values. Originality. A method for implementing a discrete perceptron that is based on the use of statistical evaluations and integer operations on discrete synaptic signals has been proposed for the first time. Practical value. The proposed approach allows avoiding the typical multiplication operation for perceptron structures, reducing computational costs. The use of a discrete basis significantly limits the value space of shift coefficients which could potentially shorten the training process. An important aspect of the results obtained is the prospects for implementing specialised artificial neural networks on platforms with limited computing resources, such as microcontrollers, programmable logic integrated circuits, and others.

Cross-linguistic Influence (CLI) in Multilingual Learners: Implications for Education

As multilingualism becomes increasingly prevalent in globalized societies, understanding the cognitive and linguistic mechanisms underpinning language acquisition is essential. This study explores cross – linguistic influence (CLI) in multilingual learners from a theoretical perspective, emphasizing its implications for linguistic theory and educational practice. Drawing upon key frameworks such as Dynamic Systems Theory, the Scalpel Model, and Multicompetence, the paper critically examines how CLI operates across multiple linguistic domains and within complex learner ecologies. Particular attention is paid to factors mediating CLI – such as language typology, proficiency, language dominance, and acquisition context – and how these factors shape multilingual development in both predictable and variable ways. The article argues for a reconceptualization of CLI not as a source of interference, but as a fundamental aspect of multilingual competence that reflects the dynamic interconnectivity of linguistic systems. The findings support a shift away from monolingual instructional models toward pedagogies that recognize and leverage the linguistic resources of multilingual learners. This theoretical inquiry lays the groundwork for future empirical research and provides valuable insights for linguistic, educators, and policymakers in the multilingual education landscape. CLI should be seen not as a hindrance but as a valuable resource, offering multilingual learners cognitive flexibility and enhanced language proficiency

Complexity, Fluency, and Accuracy in Written Works of Vietnamese Learners of English: A Replication Study

Recent studies applying Dynamic Systems Theory (DST) have shown language acquisition's non-linear, indiscrete, chaotic, and highly context-dependent nature. However, limited research has explored these dynamics in English as a Foreign Language (EFL) context. To evaluate DST’s applicability in EFL settings, this study partially replicates Larsen-Freeman’s (2006) investigation by tracking the language development of four upper-intermediate Vietnamese EFL learners. The study employed the Dynamic Description approach, in which the participants were required to take written tests every three weeks over three months. Their performance across four dimensions - accuracy, fluency, lexical complexity, and syntactic complexity- was examined through both quantitative and qualitative analyses. Although the findings revealed similarities with the original study, the learners’ development trajectories differed, proving that the learners were interacting with their surrounding EFL context. These findings underscore the significance of learning contexts on language acquisition and offer valuable insights into more context-sensitive teaching practices.

AI Merged With Human Knowledge Produces the Best Possible Weather Forecasts

AbstractA new approach called cross‐attractor transforms (Agarwal et al., 2025, https://doi.org/10.1029/2024gl110472) aims to improve weather forecasts by using neural networks to learn optimal maps between nature and imperfect numerical weather prediction (NWP) models. Unlike the latest generation of machine learning weather prediction (MLWP) models, this approach leverages prior knowledge via the known governing equations and learns only what is needed to map between that imperfect numerical model and the target system being forecasted (e.g., real‐world weather). This approach draws from the same underlying principles of dynamical systems theory and chaos theory that have been the foundation of operational NWP for the last half century, and extend upon machine learning based post‐processing efforts. The results show that an imperfect numerical model enhanced by the cross‐attractor transforms have the potential to outperform both MLWP models and NWP models post‐processed with ML, highlighting the value in merging prior knowledge with data‐driven ML methods.

Early warning signs for tipping points in systems with non-Gaussian -stable noise

Forecasting rapid, non-linear change or so-called tipping points is a major concern in ecology and environmental science. Statistical early warning signs, based on the theory of stochastic dynamical systems, are now regularly applied to observational data streams. However, the reliability of these early warning signs relies on a number of key mathematical assumptions, most notably the presence of Gaussian noise, while many ecological systems exhibit non-Gaussianity. We here show that for systems driven by non-Gaussian, -stable noise, the classical early warning signs of rising variance and autocorrelation are not supported by mathematical theory, and their use poses the danger of spurious, false-positive results. To address this, we provide a generalized approach by introducing the scaling factor as an alternative early warning sign. We show that in the case of the linear Ornstein-Uhlenbeck process, there exists a direct inverse relationship between and the bifurcation parameter, telling us that will increase as we approach the bifurcation. Our numerical simulations confirm theoretical results and show that our findings generalize well to non-linear, non-equilibrium systems often employed in ecological systems. We thus provide a generalized, robust, and broadly applicable statistical early warning sign for systems driven by Gaussian and non-Gaussian -stable noise.

Density-based recurrence measures from microstates

Recurrence analysis is a powerful tool for nonlinear time series analysis deeply rooted in the theory of dynamical systems, finding applications across many areas of science. It works by mapping recurrences of a time series or phase space trajectory into a logical matrix. Recurrence quantification analyses (RQAs) are computed from its internal structures, such as recurrence density and the distribution of diagonal and vertical lines. Here, we link the density-based recurrence measures such as determinism and laminarity to the concept of microstates. We present a way to obtain the histogram of both diagonal and vertical lines from recurrence microstates, which are small square submatrices of the recurrence matrix. This approach opens up a line of research by reframing traditional RQAs in terms of microstates. Therefore, we establish a bridge between concepts of traditional lines-based RQA and recurrence microstates, and illustrate this for various paradigmatic systems. Published by the American Physical Society 2025

Dynamic behavior and modulation instability of the generalized coupled fractional nonlinear Helmholtz equation with cubic–quintic term

Abstract In this work, the main objective is to study the dynamic behavior of the generalized coupled fractional nonlinear Helmholtz equation with cubic–quintic term, which describes soliton propagation in nonlinear optics through the theory of dynamical system. First, the original equation is transformed into an integer-order coupled partial differential equation using Atangana’s fractional derivative. Then, considering traveling wave and linear transformations, a two-dimensional planar dynamical system is constructed. Through phase portraits, stability analysis, and parameter sensitivity analysis, the dynamical behavior of the system is studied. Next, considering the dynamic behavior of the system under triangular periodic perturbation and logarithmic perturbation respectively, the reasons for the evolution of the system behavior patterns under different initial conditions are analyzed. Through qualitative analysis, we have avoided the limitations and errors of precise solution methods, and obtained the stability of the system equilibrium point under parameter changes, as well as the dynamic behavior of the system, including periodic and chaotic behaviors. Finally, by investigating the modulation instability of the system, the conditions for maintaining stability of the system are obtained through the linear stability analysis method.

Individual and environmental correlates of physical literacy sub-components in early childhood

ABSTRACT This study examined individual and environmental correlates of physical literacy sub-components among preschool-aged children (3–5 years). This cross-sectional study utilized baseline data from the PLAYshop intervention. Participants were 122 families from Alberta and British Columbia, Canada. Informed by Dynamical Systems Theory, individual (children’s age, sex, race/ethnicity) and environmental (parental education, physical activity modelling, capability, opportunity, motivation) correlates were measured via a parental questionnaire. Five fundamental movement skills (FMS; horizontal jump, hop, overhand throw, underhand throw, balance) were assessed via recorded virtual meetings using the Test of Gross Motor Development (TGMD-3) and the Movement Assessment Battery for Children (MABC-2). Children’s motivation/enjoyment/confidence of active play was parental-reported using the Preschool Physical Literacy Assessment Tool (Pre-PLAy) and children’s enjoyment was self-reported via an adapted Five Degrees of Happiness Likert scale. Regression models were conducted. Children’s age was a significant positive correlate of all FMS. Females had significantly lower scores for overhand throw, underhand throw, and parental-reported children’s motivation, compared to males. Higher parental capability was associated with higher balance scores. Higher parental education was associated with lower children’s self-reported enjoyment. Findings for race/ethnicity were mixed. Future research should explore additional correlates across settings and physical literacy sub-components to better inform physical literacy interventions.

An idiodynamic study of EFL learners’ motivational dynamics during oral practice on an ASR-based website with automatic feedback

ABSTRACT Purpose Guided by Complex Dynamic Systems Theory, this study explores the motivational dynamics of EFL learners during oral practice on an Automatic Speech Recognition website with automatic feedback. Methodology Five undergraduate students participated in oral task experiments, followed by self-rating of task motivation and stimulated recall interviews. Findings Linguistic, cognitive, metacognitive, affective, and contextual dimensions were primary variables interacting to shape learners’ motivation. Diverse and non-linear interaction patterns emerged. The study highlights the complex interplay between learner variables and AI-generated feedback, demonstrating how learners’ perceptions and expectations influence their engagement with automated learning tools. Value The findings suggest that educators should enhance learners’ critical thinking skills when using AI tools to foster adaptive interpretation of AI feedback. AI developers are encouraged to improve AI feedback accuracy and personalize support to enhance learning experiences. This research deepens understanding of motivational dynamics in AI-assisted language learning and offers implications for pedagogy and AI tool design.

Mega-Instability: Order Effect on the Fractional Order of Periodically Forced Oscillators

The stability of differential equations is one of the most important aspects to consider in dynamical system theory. Chaotic systems were classified according to stability as multi-stable systems; systems with a single stable equilibrium; bi-stable systems; and, recently, mega-stable systems. Mega-stability refers to the infinity countable nested attractors of a periodically forced non-autonomous system. Many researchers attempted to present a simple mega-stable system. In this paper, we investigated the mega-stability of periodically damped non-autonomous differential systems with the following different order cases: integer and fractional. In the case of the integer order, we generalize the mega-stable system, such that the velocity is multiplied by a trigonometrical polynomial, and we present the necessary and sufficient conditions to generated countable infinity nested attractors. In the case of the fractional order, we obtained that the fractional order of periodically damped non-autonomous differential systems has infinity countable nested unstable attractors for some orders. The mega-instability was illustrated for two examples, showing the order effect on the trajectories. In addition, and to further recent work presenting simple high dimensional mega-stable chaotic systems, we introduce a 4D mega-stable hyperchaotic system, examining chaotic and hyperchaotic behaviors through Lyapunov exponents and bifurcation diagrams.

A mechanism for the emergence of low-dimensional structures in brain dynamics

Recent neuroimaging advancements have led to datasets characterized by an overwhelming number of features. Different dimensionality reduction techniques have been employed to uncover low-dimensional manifold representations underlying cognitive functions, while maintaining the fundamental characteristics of the data. These range from linear algorithms to more intricate non-linear methods for manifold extraction. However, the mechanisms responsible for the emergence of these simplified architectures remain a topic of debate. Motivated by concepts from dynamical systems theory, such as averaging and time-scale separation, our study introduces a novel mechanism for the collapse of high dimension brain dynamics onto lower dimensional manifolds. In our framework, fast neuronal activity oscillations average out over time, leading to the resulting dynamics approximating task-related processes occurring at slower time scales. This leads to the emergence of low-dimensional solutions as complex dynamics collapse into slow invariant manifolds. We test this assumption via neural simulations using a simplified model and then enhance the complexity of our simulations by incorporating a large-scale brain network model to mimic realistic neuroimaging signals. We observe in the different cases the convergence of fast oscillatory fluctuations of neuronal activity across time scales that correspond to simulated behavioral configurations. Specifically, by employing various dimensionality reduction techniques and manifold extraction schemes, we observe the reduction of high-dimensional dynamics onto lower-dimensional spaces, revealing emergent low-dimensional solutions. Our findings shed light on the role of frequency and time-scale separation in neuronal activity, proposing and testing a novel theoretical framework for understanding the inner mechanisms governing low-dimensional pattern formation in brain dynamics.

Combined Application of CAR-T Cells and Chlorambucil for CLL Treatment: Insights from Nonlinear Dynamical Systems and Model-Based Design for Dose Finding

Background: This work presents a mechanistic nonlinear model, formulated as a system of first-order Ordinary Differential Equations, to investigate the dynamics of Chronic Lymphocytic Leukemia (CLL) under combined chemoimmunotherapy using CAR-T cells and chlorambucil. Methods: Leveraging nonlinear dynamical systems theory and a model-based design approach, we derive optimal dosing strategies through extensive in silico simulations, providing hemato-oncologists with actionable tools to refine CLL treatment. The model captures the short- and long-term impacts of both therapies on leukemia cell populations, enabling precise predictions of therapeutic outcomes. Results: By analyzing local and global system dynamics, we establish sufficient conditions for dosing and protocol design, offering a framework to optimize therapies based on individual patient responses. Comparisons of dose-escalation and -de-escalation strategies further demonstrate potential trajectories, such as complete eradication, partial response, or relapse, providing data-driven guidance for improving patient care. Conclusions: This study highlights the power of mathematical modeling in blood cancer research, enhancing the development of personalized and effective CLL treatment regimens.

Exploring temporal variations in anxiety in multilingual English teachers: an idiodynamic approach

Background and objectivesThe role of anxiety in second language acquisition (SLA) research is well established. Following the dynamic turn in SLA research [1], there has been a significant increase in studies examining anxiety from a dynamic and temporal perspective. However, while most studies focus on student anxiety, research on the temporal dimensions of language teachers’ anxiety remains limited, particularly in studies utilizing Complex Dynamic Systems Theory (CDST)-compatible methods. This study aims to address this gap by examining the dynamic anxiety of two English teachers using an idiodynamic approach, with the overarching purpose of providing a deeper understanding of how their anxiety fluctuates during and across teaching sessions.MethodsData were collected from two experienced multilingual English teachers through idiodynamic self-ratings, reflective journals, and semi-structured interviews. Descriptive and thematic analyses were conducted to identify patterns of anxiety fluctuations within and across participants.ResultsThe analysis revealed fluctuations in anxiety levels both within and across participants. Factors such as problems with instruction, student distractions, and classroom management contributed to anxiety fluctuations, whereas experience, emotion regulation strategies, and active student participation helped stabilize anxiety.ConclusionThis study contributes to the evolving field of anxiety research by examining teacher anxiety from a dynamic perspective. The findings underscore the importance of addressing fluctuating anxiety levels in teacher training programs to enhance classroom effectiveness and promote teacher well-being.

The relationship between complexity, accuracy and fluency in L2 English speech: Individual differences and dynamic patterns

This study examined the relationship between complexity, accuracy and fluency (CAF), using longitudinal data. Conducted from the perspective of complex dynamic systems theory (CDST), this research adopted four CAF general measures to track the development of five Chinese undergraduates’ English speech over a 15-week period. LOWESS graphs supported by correlation analyses showed that there were individual differences in CAF relations. Different trade-off effects were found in the CAF development of four individuals. One learner improved in lexical complexity at the expense of accuracy, another learner improved in accuracy at the cost of lexical complexity, one student made progress in syntactic complexity but sacrificed fluency, and one improved in accuracy and lexical complexity while compromising fluency and syntactic complexity, respectively. Furthermore, the use of moving correlations demonstrated that CAF relations changed dynamically over time, revealing eight identified change patterns. These patterns exhibited varying degrees of variability, ranging from highest to medium to low-medium to lowest. Six patterns involved state changes, transitioning from a competitive to supportive relationship, for example.

Study of Two Sinusoidal Forcing Terms in a Geo-KdV Model

In this study, a Geo-KdV model is considered which is typically an extended KdV Equation with an extra term responsible for the Coriolis effect on wave dynamics, with the Coriolis parameter denoted by [Formula: see text]. While most of the studies available in the literature treat [Formula: see text] as constant, in this study, the model is investigated for its stability for a range of values of [Formula: see text] by employing certain standard tools from bifurcation analysis such as phase portraits, bifurcation maps and the Lyapunov exponents. Based on the analysis, it is found that the model can exhibit chaotic behavior for certain critical values of [Formula: see text]. Furthermore, motivated by studies in plasma physics, seismology and other related areas available in the literature, two distinct forcing terms, namely, [Formula: see text] and [Formula: see text] are considered as perturbations in the model. Here, [Formula: see text] and [Formula: see text] denote the forcing and the frequency parameters, respectively. Also, [Formula: see text] is time and [Formula: see text] is the free surface elevation included in the model equation. It’s important to note that while the forcing terms may seem similar, they have different effects on the model problem; [Formula: see text] results in a two-dimensional system, while [Formula: see text] leads to a three-dimensional system. A comparative study of these forcing terms is done for certain critical values of these parameters using the standard theory of dynamical systems. It is found that the system exhibits aperiodic, quasi-periodic and chaos-like behaviors for these critical values of the parameters. Confirmation of chaos-like behavior under various conditions in the Geo-KdV model is established by employing bifurcation analysis tools.

Dynamical systems model of embodied memory in early human infancy.

Memory is formed through repeated action and perception. The primitive manifestation of this type of memory in infants has been observed through a procedure called mobile paradigm. Three-month-old infants can retain behavioral changes during interaction with a mobile for a week without reminders, and this retention can be prolonged for 2-4 weeks with reminders. However, precisely what infants can remember and how memory retention and reactivation work at this young age remains unclear. In this article, we introduce dynamical systems models that replicate this form of memory by incorporating two dynamic properties. The first dynamic process is responsible for creating and retaining a memory of the experience of controlling movement generation to interact with the environment. While this memory can be used in retention tests of learned behaviors, it undergoes a gradual decay. The second property involves asymmetric bifurcation, through which a memory of the circular causality between self-movement and environmental events is formed. This memory, related to agency, persists and enables reactivation of the decayed memory of learned behaviors. Our simulation suggests that memory emerges as an embodiment of internal dynamics through the repetition of action and perception. The form of retained memory in the mobile paradigm is comparable to that in the A-not-B error and habituation-dishabituation tasks. The theory of dynamical systems unifies experimental results regarding memory in early life as an embodied process, with the maturation of the memory system originating from the embodied process between the brain, body, and environment. (PsycInfo Database Record (c) 2025 APA, all rights reserved).