Dynamical Systems Theory Research Articles

Bifurcations, chaotic behavior, sensitivity analysis, and various soliton solutions for the extended nonlinear Schrödinger equation

In this manuscript, our primary objective is to delve into the intricacies of an extended nonlinear Schrödinger equation. To achieve this, we commence by deriving a dynamical system tightly linked to the equation through the Galilean transformation. We then employ principles from planar dynamical systems theory to explore the bifurcation phenomena exhibited within this derived system. To investigate the potential presence of chaotic behaviors, we introduce a perturbed term into the dynamical system and systematically analyze the extended nonlinear Schrödinger equation. This investigation is further enriched by the presentation of comprehensive two- and 3D phase portraits. Moreover, we conduct a meticulous sensitivity analysis of the dynamical system using the Runge–Kutta method. Through this analytical process, we confirm that minor fluctuations in initial conditions have only minimal effects on solution stability. Additionally, we utilize the complete discrimination system of the polynomial method to systematically construct single traveling wave solutions for the governing model.

Evolutionary game analysis of stakeholders’ decision-making behavior in agricultural data supply chain

The significance of agricultural information sharing in fostering agricultural development cannot be overstated. This practice plays a pivotal role in disseminating cutting-edge agricultural technologies, cultivation methods, and pest control strategies, empowering farmers with valuable knowledge to enhance crop yield and quality. Moreover, it aligns with government objectives of resource sharing and addressing gaps, contributing to the advancement of agricultural modernization and the development of the industry chain. Despite its inherent benefits, the practical implementation of agricultural information sharing faces challenges. Stakeholders engaged in information sharing often prioritize individual benefits, potentially leading to a decline in agricultural information quality and the inefficient use of experimental resources. To confront this issue, the present research establishes a three-party evolutionary game model comprising an agricultural product data sharing platform, agricultural data providers, and agricultural data consumers. Leveraging dynamic system theory, the model analyzes the evolutionary stable strategies of stakeholders and investigates the critical factors influencing the strategic choices of these three parties. Experimental findings underscore the pivotal role of participants’ initial strategies, regulatory intensity, reward and punishment mechanisms, and information feedback in shaping stakeholder decision-making behavior. Implementation of measures such as heightened scrutiny of information on the sharing platform and fostering consumer trust in data emerges as imperative for enhancing system stability. These actions are essential for constructing an efficient and reliable information-sharing ecosystem, thereby facilitating the sustainable development of modern agriculture.

Identifying regime shifts, transients and late warning signals for proactive ecosystem management

Conservation Biology fosters the study of Earth's ecosystems and biodiversity aiming at protecting species and their habitats from menaces causing the erosion of biotic interactions and extinctions. Its ultimate goal is to preserve biodiversity and promote sustainable ecological management maintaining both ecosystem's resilience and services. Ecosystems display complex patterns in time and space due to the intrinsic nonlinear nature of their interactions and can suffer regime shifts driven by the agents of global change. During the last decades, Ecology has turned from the equilibrium metaphor to the paradigm of non-equilibrium dynamics. This involves putting into the scene multiple stable states, nonlinear regime shifts, stochasticity, and ecological transients. These aspects are also crucial for biological conservation since they play a fundamental role in species' persistence, ecosystems' resilience, and in detecting warning signals prior to either the collapse or the recovery of the ecosystem. In this contribution, we discuss ecological regime shifts caused by tipping points in real ecosystems. Then, we provide information on some known dynamical features from theoretical ecology and dynamical systems theory associated to tipping points, mainly given by transient phenomena and the characteristic statistical patterns tied to early warning signals. These features are illustrated with a single-species mathematical model including facilitation and immigration. We also introduce and provide evidence of late warning signals as a way to identify when a tipping point has been surpassed but the system still remains in a transient state and recovery may be still possible. Our main goal is to near non-equilibrium concepts in Ecology to the conservationist community and promote bridges between such concepts and the management and conservation of ecosystems.

Spatial dispersal in chemostat systems with agent-based asymmetry

This paper considers chemostat consumer-resource systems in which the consumer disperses between spatial patches and acts as an agent. Using the theory of dynamical systems and the method of graphs, we demonstrate global stability of steady states in the model. It is shown that dispersal of the consumer and clustering mode of patches are important for persistence of the consumer, while asymmetry in the dispersal determines the final distribution of consumer in the system. Moreover, appropriate asymmetry could make the consumer persist in sink patches, and could make the consumer approach a total population abundance higher than that without dispersal. A novel finding of this work is that agent-based selection on asymmetry could make the consumer evolve to the maximal abundance. Numerical simulations on the model reproduce radiograph/CT of COVID-19 patients in both figures and animations. Our research has potential applications in computer-aided diagnosis and treatment.

The Dynamical Footprint of Year‐Round North American Weather Regimes

AbstractWeather regimes have been defined over multiple regions and used in a range of practical applications, including subseasonal‐to‐seasonal forecasting and climate model evaluation. Despite their widespread use, the extent to which regimes reflect physical modes of the atmosphere is seldom investigated. Here, we adopt a year‐round classification of four North American weather regimes, with a fifth “no regime” class, and leverage dynamical systems theory to investigate their dynamical properties. We find that when the atmospheric flow is assigned to a regime, it displays persistent characteristics and a lifecycle‐like temporal evolution. We further find that, regardless of season, these characteristics are enhanced when the atmospheric flow displays a comparatively strong projection onto the cluster‐mean of the regime to which it is assigned (while the reverse is true for a weaker projection). We interpret these results as evidence that the four North American weather regimes are physically‐meaningful, with a clear dynamical footprint.

Revisiting complex dynamic systems theory: Empowering language teachers and teaching

AbstractThis article revisits complex dynamic systems theory (CDST) and provides a new synthesis that, the authors argue, may empower language teachers. The particular focus is on the interplay between change and stability in complex dynamic systems, including language teaching and learning. The article identifies four key dynamical properties of complex dynamic systems, which reflect change, stability, and the interplay between these two. The dynamical properties are historicity, adaptiveness, nonlinearity, and emergence. The authors associate these dynamic properties with four recognisable types of activity: normative, contingent, creative, and purposeful teaching and learning. The central argument is that language teaching and learning are interconnected, and language teaching that promotes these four types of teaching and learning activity may also promote opportunities for language learning. The authors conclude with a discussion of how teachers may use this CDST perspective to reflect on three aspects of their professional context—teaching, language, and agency—and how such reflection, followed by action, may promote opportunities for language learning in their contexts.

The dynamics and mediating factors of students’ emotional and social engagement in a project-based writing course

Studies of student engagement in language learning have burgeoned in the last three decades. However, its dynamic trajectory and the attendant mediating factors leading to various outcomes in project-based language learning (PBLL) have been underexplored. PBLL emphasizes social communication and engagement as students complete complex tasks over an extended period of time, making it distinct from traditional teacher-centered instruction. With this focus in mind, our study draws on Complexity of Dynamic Systems Theory (CDST) to examine the longitudinal development of emotional and social engagement among Chinese EFL students in an English for Academic Purposes (EAP) writing course, and to explore factors accounting for possible changes in those two types of engagement. Using three sets of questionnaires to track student engagement over the course of a learning project, we found an overall increase of emotional and social engagement during students’ learning process, despite a slight dip at the midway point. A follow-up interview showed that engagement changes were mainly driven by peer influence, task completion in PBLL, leadership, and preference for PBLL. These findings provide insight into the dynamics of student engagement in PBLL settings in China and have implications for EAP writing pedagogy.

Multi-Time-Scale Analysis of Chaos and Predictability in vTEC

Theoretical modelling of the local ionospheric medium (LIM) is made difficult by the occurrence of irregular ionospheric behaviours at many space and time scales, making prior hypotheses uncertain. Investigating the LIM from scratch with the tools of dynamical system theory may be an option, using the vertical total electron content (vTEC) as an appropriate tracer of the system variability. An embedding procedure is applied to vTEC time series to obtain the finite dimension (m∈N) of the phase space of an LIM-equivalent dynamical system, as well as its correlation dimension (D2) and Kolmogorov entropy rate (K2). In this paper, the dynamical features (m,D2,K2) are studied for the vTEC on the top of three GNSS stations depending on the time scale (τ) at which the vTEC is observed. First, the vTEC undergoes empirical mode decomposition; then (m,D2,K2) are calculated as functions of τ. This captures the multi-scale structure of the Earth’s ionospheric dynamics, demonstrating a net distinction between the behaviour at τ≤24h and τ≥24h. In particular, sub-diurnal-scale modes are assimilated to much more chaotic systems than over-diurnal-scale modes.

Experimental Trajectories of Convergence and Divergence Processes of Russian Regions Population Incomes Inequality

The study is devoted to the problem of differentiation of incomes of the population of Russia's regions. The goal of the work is to develop a methodology for analyzing the processes of differentiation of incomes of the population in Russia's regions based on the theory of dynamic systems and machine learning, and its testing on recent analytical data. The research hypothesis lies in the assumption of the simultaneous coexistence of processes of convergence and divergence of processes of differentiation of incomes of the population of Russia's regions, depending on external and internal factors. These processes are the subject of the research. The information base is the Federal State Statistics Service's data on the values of the Gini index of 80 regions for the period from 1995 to 2018. To construct experimental trajectories, in addition to the Gini index, two independent dynamic variables were used - its first and second derivatives, which made it possible to construct 3 different spaces of states (from one-dimensional to three-dimensional). Using the k-means clustering method, the entire observed set of states was divided into 5 clusters, the number of which was previously determined by the “elbow method” test. As a result of the calculations, the predominance of convergent processes over divergent ones during the studied period was proven. It was found that the individual trajectories of certain regions in the space of state differ significantly: the trajectories of some regions can be localized within only one cluster, while some parts of the trajectories of others can belong to up to 4 clusters. The majority of the trajectories are located within 2-3 clusters. The theoretical significance of the results obtained lies in deepening the understanding of the regional specifics of the dynamic changes in the differentiation of income of the population of the constituent entities of the Russian Federation. The practical significance of the research results lies in the expansion of instrumental support for decision-making in the implementation of the state policy in the field of regulating the differentiation of income of the population at the regional level.

Clinical Tumor Dormancy.

This chapter summarizes clinical evidence on tumor dormancy, with a special focus on our research supporting the role of dormancy both in local and distant recurrence of breast cancer following mastectomy. Starting from these premises, we propose a model of neoplastic development that allows us to elucidate several relevant clinical phenomena, including the mammographic paradox, the significance of ipsilateral breast tumor recurrence after conservative surgery, and the effect of surgeries performed after the removal of the primary. We will discuss the biological implications of the dormancy-based model, which are at odds with Somatic Mutation Theory. We will then review new models, alternatives to the Somatic Mutation Theory, for cancer development, with special emphasis on the Dynamic System Theory and the originality of its conceptual approach. Finally, we will put particular emphasis on the view of cancer development as a tissue-level process. We believe that this will help harmonize the molecular biology research with the new conceptual approach and bridge the knowledge gap on dormancy between bench and bedside.

Dynamical behavior-based approach for the evaluation of treatment efficacy: The case of immuno-oncology.

Sophistication of mathematical models in the pharmacological context reflects the progress being made in understanding physiological, pharmacological, and disease relationships. This progress has illustrated once more the need for advanced quantitative tools able to efficiently extract information from these models. While dynamical systems theory has a long history in the analysis of systems biology models, as emphasized under the dynamical disease concept by Mackey and Glass [Science 197, 287-289 (1977)], its adoption in pharmacometrics is only at the beginning [Chae, Transl. Clin. Pharmacol. 28, 109 (2020)]. Using a quantitative systems pharmacology model of tumor immune dynamics as a case study [Kosinsky et al., J. Immunother. Cancer 6, 17 (2018)], we here adopt a dynamical systems analysis to describe, in an exhaustive way, six different statuses that refer to the response of the system to therapy, in the presence or absence of a tumor-free attractor. To evaluate the therapy success, we introduce the concept of TBA, related to the Time to enter the tumor-free Basin of Attraction, and corresponding to the earliest time at which the therapy can be stopped without jeopardizing its efficacy. TBA can determine the optimal time to stop drug administration and consequently quantify the reduction in drug exposure.

EMBED IN ENSEMBLE TO RIGOROUSLY AND ACCURATELY HOMOGENIZE QUASI-PERIODIC MULTI-SCALE HETEROGENEOUS MATERIAL

AbstractFor microscale heterogeneous partial differential equations (PDEs), this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with finite scale separation: no scale separation limit is required. A key innovation herein is to analyse the ensemble of all phase-shifts of the heterogeneity. Dynamical systems theory then frames the homogenization as a slow manifold of the ensemble. Depending upon any perceived scale separation within the quasi-periodic heterogeneity, the homogenization may be done in either one step or two sequential steps: the results are equivalent. The theory not only assures us of the existence and emergence of an exact homogenization at finite scale separation, it also provides a practical systematic method to construct the homogenization to any specified order. For a class of heterogeneities, we show that the macroscale homogenization is potentially valid down to lengths which are just twice that of the microscale heterogeneity! This methodology complements existing well-established results by providing a new rigorous and flexible approach to homogenization that potentially also provides correct macroscale initial and boundary conditions, treatment of forcing and control, and analysis of uncertainty.

Modelling the outbreak of epidemic based on system dynamics coupled text mining

Amidst the rapid pace of globalization and the rising density of populations, the prevalence of epidemic outbreaks has emerged as a heightened cause for apprehension. The emergence and spread of epidemic are determined by the coupling of multiple factors. Herewith, the method of text mining was used to extract these factors, including vaccination, detection, and physical protection. An evolution model considering multiple factors based on system dynamics theory was established to simulate epidemic dynamics. The results of numerical experiment showed that this model would effectively nowcast the epidemic dynamics. The heterogeneous efficacy of multiple interventions on containing the epidemic was estimated, where personal protection, the vaccination rate, and isolation control had negative feedback effects on epidemic evolution; physical protection showed the strongest effect while isolation presented the weakest ones. On this basis, countermeasures to effectively control the outbreak are summarized.

The index theory for multivalued dynamical systems with applications to reaction-diffusion equations with discontinuous nonlinearity

The index theory for multivalued dynamical systems with applications to reaction-diffusion equations with discontinuous nonlinearity

Новые технологии естественного интеллекта в задачах автоматизации рассуждений

One of the most important challenges that humanity will have to answer in the 21st century is its ability to master intelligence. This provides for the elaboration of a series of questions, including the following: Are there other, non-humanoid intellectual beings? In which variants, in relation to possible extra-human forms of intelligence, is human intelligence positioned (surpasses, lags behind, competes)? Using the topic of new technologies of natural intelligence in the automation of reasoning, the authors propose to shift the emphasis from the focus on the development of artificial intelligence as a competitor and even a threat to man in its strong version, to the task of a complex development of intelligence as a cosmic phenomenon. This focus provides for such a work plan, where the audit of natural intelligence should be the beginning. An assumption is made that the untapped potential of natural intelligence is very large, and its insufficient development was due to significant advances in computer automation. The authors propose to consider the prospects that open up from the use of categorical methodology in reasoning, and especially in their automation. Categories are defined by cognitive units that organize reasoning, and concepts are forms of thought that convey the meaning and content of reasoning. The experiments of implementing categorical methodology in dual and triadic constructions are discussed. It is stated that the potential of categorical schemes in the forms of triads is not sufficiently realized. The authors proceed from the assumption of a significant methodological potential contained in the theory of dynamic information systems (TDIS, DIS). TDIS can play the role of a base for the deployment of a categorical methodology. An example is given demonstrating the operation of a TDIS device. In conclusion, a summary is made about the expediency of the complex human development of intelligence, implemented in various ways and on a variety of natural and artificial media. A more important task, in comparison with the isolated improvement of artificial intelligence to the level of its strong version, is the work on the integration of individual intelligences. In principle, we can talk about a tremendous success in combining the computing power of computers in cloud technologies, but this is not the integration of intelligence.

Discovering State-Space Representation of Dynamical Systems From Noisy Data

Discovering State-Space Representation of Dynamical Systems From Noisy Data

Inverse shadowing characteristic in Z-group

In the realm of dynamical systems theory, shadowing plays a crucial role. Structurally stable diffeomorphisms exhibit a noteworthy characteristic known as the inverse shadowing characteristic, which is investigated within the context of continuous methods. On compact manifolds, hyperbolic homeomorphisms are demonstrated to possess both inverse shadowing and bi-shadowing characteristics, particularly concerning a class of δ methods. These methods are described as continuous mappings from the manifold into the space of bi-infinite sequences within the manifold, utilizing the product topology. Additionally, the shadowing characteristic of the Lipschitz inverse is explored concerning two distinct classes of approaches, which produce pseudo-trajectories for dynamical systems. In our research, we establish that the characteristic of inverse shadowing can be derived from several fundamental dynamical system characteristics, including structural stability, transversality, Anosov characteristics, expansivity, continuum-wise expansiveness, and expansion.

Breaking New Ground: Applying Complex Dynamic Systems Theory to Domestic Research on Language Attrition

Breaking New Ground: Applying Complex Dynamic Systems Theory to Domestic Research on Language Attrition

PHASE SYNCHRONIZATION OF PARTICLES AT CYCLOTRON RESONANCES

Subject and Purpose. The effects considered concern phase synchronization of electrons in an ideal plasma subjected to the action of an external uniform, d. c. magnetic field. Two modes of the synchronization are discussed, specifically one by an external electromagnetic field and the other by the cyclotron radiation emitted by the electrons. The purpose is to compare these forms of synchronization and their effects on plasma stability. Methods and Methodology. The plasma is represented as a set of coupled oscillators whose dynamics is described via coupled differential equations. Assuming the coupling between the oscillators to be weak we find analytical solutions to the equation, further performing a stability analysis which exploits standard approaches of the dynamical systems theory. The solutions found are validated through corresponding numerical simulations. Results. As has been found, an external electromagnetic wave may be capable of guiding the particles toward phase synchronization, which can lead to formation of phased bunches. This mechanism of particle grouping may prove to be more efficient, in terms of scale times of synchronization, if compared with known mechanisms exploiting relativistic effects. Additionally, we show that the cyclotron radiation emitted by the charged particles (which is often disregarded because of its smallness) can lead to self-phase synchronization of the electrons. Moreover, should the density of charged particles in the ensemble be sufficiently high, an instability can arise, potentially disrupting the ensemble. Estimates have been provided of the level of random fluctuations capable of undermining the synchronization process and plasma dynamics stabilization. Conclusions. The most significant finding of this analysis is the emergence of low-frequency oscillations in the charged oscillators set, followed by an onset of the plasma instability when the plasma density exceeds a certain critical value. Within that scenario, the ensemble of oscillators sitting in the external magnetic field is no longer held together by the field. The effect should be taken into account in applications related to plasmas of a relatively high density.

The interaction of factors in constructing English learning motivation of China’s government-sponsored overseas academic visiting candidates on an official preparatory program

The present study investigates the English learning motivation of China’s government-sponsored overseas academic visiting candidates on an official intensive English preparatory program. A structural equation model (SEM) analysis was conducted on the results of a 33-item questionnaire survey taken by 632 such candidates, most of whom were university academics. By establishing a SEM model for the general sample and four sub-models for its sub-samples, the study delineates the complex interaction of the components in shaping this population’s English learning motivation against the backdrop of China’s grand socio-educational ambition. It also reveals some nuanced differences in the path coefficients in this motivational complex within each of its two sub-sample sets: the candidates with humanities and social science backgrounds vs. those with science backgrounds and the candidates from an institution or program on China’s Double First Class initiative vs. those not. These research findings may help a better understanding of the English learning ecology in today’s China. Theoretically, this study reinforces the usefulness of the prevailing L2 Motivational Self System framework while at the same time accentuating its socio-contextual variance; it also illuminates the future direction pertaining to the application of the Complex Dynamic Systems theory.