Dynamical Systems Perspective Research Articles

Understanding Controller-Pilot Interaction Dynamics in The Context of Air Traffic Control

LiteratureNew capabilities to modernize the U.S. National Airspace System (NAS) include support of real-time information streams derived from many data sources across the NAS. As an emergent proper...

Qualitative study of effects of vorticity on traveling wave solutions to the two-component Zakharov–Itō system

In this paper, we qualitatively study effects of vorticity on traveling wave solutions to the two-component Zakharov–Itō system from the perspective of dynamical systems and show that the vorticity (c is the wave speed) is the critical vorticity. Based on this critical vorticity, we obtain all possible phase portraits of the system under exact explicit parameter conditions. Then we not only show the existence of all bounded traveling wave solutions including solitary wave solutions, periodic wave solutions, kinklike (antikink) wave solutions and compactons, under corresponding exact explicit parameter conditions, but also obtain the exact expressions of solitary wave solutions and blow-up solutions (unbounded solutions). The previous results are extended.

Perturbations of the Lambda-CDM model in a dynamical systems perspective

The observational success and simplicity of the ΛCDM model, and the explicit analytic perturbations thereof, set the standard for any alternative cosmology. It therefore serves as a comparison ground and as a test case for methods which can be extended and applied to other cosmological models. In this paper we introduce dynamical systems and methods to describe linear scalar and tensor perturbations of the ΛCDM model, which serve as pedagogical examples that show the global illustrative powers of dynamical systems in the context of cosmological perturbations. We also study the asymptotic properties of the shear and Weyl tensors and discuss the validity of the perturbations as approximations to the Einstein field equations. Furthermore, we give a new approximation for the linear growth rate, f(z) = d ln δ/d ln a = Ω6/11m − 1/70(1−Ωm)5/2, where z is the cosmological redshift, Ωm = Ωm(z), while a is the background scale factor, and show that it is much more accurate than the previous ones in the literature.

Detailed qualitative dynamical analysis of a cosmological Higgs field

A scalar cosmological Higgs field is expected to exist in our universe in order to create inertial mass. Some results obtained at LHC suggest that this idea must be reconsidered. The cosmological effects of scalar fields have been proposed as a mechanism to drive the evolution of the universe in various scenarios. In this paper we investigate, from the dynamical systems perspective, the evolution of a Universe consisting of a matter component $$\rho $$ together with a scalar field $$\phi $$ exhibiting a quartic polynomial self-interacting potential. We consider an homogeneous and isotropic flat Friedmann–Robertson–Walker metric. Center Manifold Theory is employed to investigate the dynamics near a non-hyperbolic critical point. We prove that there are two possible late time attractors corresponding to stable de Sitter solutions.

Shear stress-driven flow: the state space of near-wall turbulence as

An inner-scaled, shear stress-driven flow is considered as a model of independent near-wall turbulence as the friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\rightarrow \infty$. In this limit, the model is applicable to the near-wall region and the lower part of the logarithmic layer of various parallel shear flows, including turbulent Couette flow, Poiseuille flow and Hagen–Poiseuille flow. The model is validated against damped Couette flow and there is excellent agreement between the velocity statistics and spectra for the wall-normal height $y^{+}<40$. A near-wall flow domain of similar size to the minimal unit is analysed from a dynamical systems perspective. The edge and fifteen invariant solutions are computed, the first discovered for this flow configuration. Through continuation in the spanwise width $L_{z}^{+}$, the bifurcation behaviour of the solutions over the domain size is investigated. The physical properties of the solutions are explored through phase portraits, including the energy input and dissipation plane, and streak, roll and wave energy space. Finally, a Reynolds number is defined in outer units and the high-$Re$ asymptotic behaviour of the equilibria is studied. Three lower branch solutions are found to scale consistently with vortex–wave interaction (VWI) theory, with wave forcing localising around the critical layer.

Thoughts on the Launching of a New Journal: A Complex Dynamic Systems Perspective

The launching of The Journal for the Psychology of Language Learning is a signal achievement. I begin this commentary by speculating on why it is that the Psychology of Language Learning (PLL) has enjoyed such vigor of late. I expect that one reason is the coming together of a critical mass of researchers and strong leaders over their shared interests. A second reason may be that a new way of looking at familiar phenomena was introduced in the form of complex dynamic systems theory (CDST). Building on this supposition, I proceed to recommend extending CDST thinking in some new ways in PLL. These ways are phenomenological, relational, processual, and transdisciplinary. I conclude by urging the PLL community to remain connected with other areas of applied linguistics so that it may continue to contribute to a knowledge-building community.

Abundant Dynamical Behaviors of Bounded Traveling Wave Solutions to Generalized θ-Equation

We study existence and dynamics of bounded traveling wave solutions to generalized $$\theta $$ -equation from the perspective of dynamical systems. We obtain bifurcation of traveling wave solutions for the equation, prove the existence of several types of bounded traveling wave solutions, including solitary wave solutions, periodic wave solutions, peakons, periodic cusp waves, compactons and kink-like (antikink-like) waves, and derive some of their exact expressions. Most importantly, we confirm abundant dynamical behaviors of the traveling wave solutions to the equation, which are summarized as follows: (1) We confirm that three types of orbits give rise to solitary wave solutions, that is, the homoclinic orbit passing the singular point, the composed homoclinic orbit which is comprised of three heteroclinic orbits of the associated system, and the composed homoclinic orbit which is comprised of two heteroclinic orbits and tangent to the singular line at the singular point of the associated system. (2) We confirm that four types of orbits correspond to periodic wave solutions, that is, the periodic orbit surrounding a center, the periodic orbit surrounding two connected homoclinic orbits, the composed periodic orbit which is comprised of two heteroclinic orbits of the associated system, and the homoclinic orbit of the associated system which is tangent to the singular line at the singular point of the associated system. (3) We confirm that two types of orbits correspond to periodic cusp waves, that is, the semiellipse orbit surrounding a center, and the semiellipse-like orbit surrounding two connected homoclinic orbits. (4) We confirm that two families of periodic orbits, which surround two connected homoclinic orbits and are comprised of two heteroclinic orbits of associated system, respectively, and the composed homoclinic orbit, which is comprised of two heteroclinic orbits and tangent to the singular line at the singular point of associated system, have envelope.

A new dynamical systems perspective on atmospheric predictability: Eastern Mediterranean weather regimes as a case study

The atmosphere is a chaotic system displaying recurrent large-scale configurations. Recent developments in dynamical systems theory allow us to describe these configurations in terms of the local dimension-a proxy for the active number of degrees of freedom-and persistence in phase space, which can be interpreted as persistence in time. These properties provide information on the intrinsic predictability of an atmospheric state. Here, this technique is applied to atmospheric configurations in the eastern Mediterranean, grouped into synoptic classifications (SCs). It is shown that local dimension and persistence, derived from reanalysis and CMIP5 models' daily sea-level pressure fields, can serve as an extremely informative qualitative method for evaluating the predictability of the different SCs. These metrics, combined with the SC transitional probability approach, may be a valuable complement to operational weather forecasts and effective tools for climate model evaluation. This new perspective can be extended to other geographical regions.

An Autobiographical Study of Language Teacher’s Perceived Psychological Dynamics: Methodological Issues and Insights

Psychological research in second language acquisition (SLA) is a growing field. Much of this research has primarily focused on examining the language learner with comparatively little emphasis on exploring the language teacher. Moreover, psychological research informed by process-oriented approaches views individuals’ psychological constructs stable individual difference variables. Recently, there has been a growing interest in the complex dynamic systems perspective, which has led researchers to focus increasingly on the dynamic nature of individuals’ psychological variables. This study explores the psychological dynamics of two male participants working at tertiary-level as English language teachers in Pakistan over the long-term timescale of years. Data were generated using autobiographical narratives. An inductive approach, which is inspired by Grounded Theory was then used to analyze the data. The findings demonstrate both stability and change in teachers’ experiences, thus suggesting the dynamic nature of their psychology. The paper concludes by discussing the methodological challenges facing future research on individual’s psychological dynamics. Keywords: autobiographical narratives, complexity perspective, dynamism, English language teachers, psychology

Using State Space Grids for Modeling Temporal Team Dynamics.

We outline the potential of dynamics systems theory for researching team processes and highlight how state space grids, as a methodological application rooted in the dynamic systems perspective, can help build new knowledge about temporal team dynamics. Specifically, state space grids visualize the relationship between two categorical variables that are synchronized in time, allowing the (team) researcher to track and capture the emerging structure of social processes. In addition to being a visualization tool, state space grids offer various quantifications of the dynamic properties of the team system. These measures tap into both the content and the structure of the dynamic team system. We highlight the implications of the state space grid technique for team science and discuss research areas that could benefit most from the method. To illustrate the various opportunities of state space grids, we provide an application example based on coded team interaction data. Moreover, we provide a step-by-step tutorial for researchers interested in using the state space grid technique and provide an overview of current software options. We close with a discussion of how researchers and practitioners can use state space grids for team training and team development.

A dynamical systems perspective on driver behavior

Dynamical systems (DS) theoretical and methodological approaches have furthered our understanding of human development and behavior across many different domains, but have not yet been applied to driver behavior. Using a DS lens, a new theory of driver behavior is proposed, the phase transition framework (PTF), and then applied to understanding how novice drivers develop. The PTF can facilitate new lines of research by providing an individual-level explanatory account that yields the widely observed and poorly understood aggregate declines in novice drivers’ crash rates in the early months of licensure. For the purpose of the PTF, learning to drive is defined as changes in the psychological system integral to the acquisition, refinement, automation, and maintenance of competencies necessary for safe driving. In the PTF, the greatest reductions in population-level collision rates observed in the early months of the post-licensure period are hypothesized to be due to qualitative cognitive reorganizations (e.g., adoption of strategies that reduce risk) that cause abrupt shifts in crash risk trajectories into lower risk strata followed by refinement of strategy use and deployment through real-world experience. Critically, the PTF differs from other theories of driver behavior in that it holds that drivers’ behavioral development is self-organizing and emergent.

Enhanced Waddington landscape model with cell-cell communication can explain molecular mechanisms of self-organization.

The molecular mechanisms of self-organization that orchestrate embryonic cells to create astonishing patterns have been among major questions of developmental biology. It is recently shown that embryonic stem cells (ESCs), when cultured in particular micropatterns, can self-organize and mimic the early steps of pre-implantation embryogenesis. A systems-biology model to address this observation from a dynamical systems perspective is essential and can enhance understanding of the phenomenon. Here, we propose a multicellular mathematical model for pattern formation during in vitro gastrulation of human ESCs. This model enhances the basic principles of Waddington epigenetic landscape with cell-cell communication, in order to enable pattern and tissue formation. We have shown the sufficiency of a simple mechanism by using a minimal number of parameters in the model, in order to address a variety of experimental observations such as the formation of three germ layers and trophectoderm, responses to altered culture conditions and micropattern diameters and unexpected spotted forms of the germ layers under certain conditions. Moreover, we have tested different boundary conditions as well as various shapes, observing that the pattern is initiated from the boundary and gradually spreads towards the center. This model provides a basis for in-silico modeling of self-organization. https://github.com/HFooladi/Self_Organization. Supplementary data are available at Bioinformatics online.

Descriptive Analysis of the Interactive Patterning of the Vocalization Subsystems in Healthy Participants: A Dynamic Systems Perspective.

Purpose Normative data for many objective voice measures are routinely used in clinical voice assessment; however, normative data reflect vocal output, but not vocalization process. The underlying physiologic processes of healthy phonation have been shown to be nonlinear and thus are likely different across individuals. Dynamic systems theory postulates that performance behaviors emerge from the nonlinear interplay of multiple physiologic components and that certain patterns are preferred and loosely governed by the interactions of physiology, task, and environment. The purpose of this study was to descriptively characterize the interactive nature of the vocalization subsystem triad in subjects with healthy voices and to determine if differing subgroups could be delineated to better understand how healthy voicing is physiologically generated. Method Respiratory kinematic, aerodynamic, and acoustic formant data were obtained from 29 individuals with healthy voices (21 female and eight male). Multivariate analyses were used to descriptively characterize the interactions among the subsystems that contributed to healthy voicing. Results Group data revealed representative measures of the 3 subsystems to be generally within the boundaries of established normative data. Despite this, 3 distinct clusters were delineated that represented 3 subgroups of individuals with differing subsystem patterning. Seven of the 9 measured variables in this study were found to be significantly different across at least 1 of the 3 subgroups indicating differing physiologic processes across individuals. Conclusion Vocal output in healthy individuals appears to be generated by distinct and preferred physiologic processes that were represented by 3 subgroups indicating that the process of vocalization is different among individuals, but not entirely idiosyncratic. Possibilities for these differences are explored using the framework of dynamic systems theory and the dynamics of emergent behaviors. A revised physiologic model of phonation that accounts for differences within and among the vocalization subsystems is described. Supplemental Material https://doi.org/10.23641/asha.7616462.

Gaze training supports self-organization of movement coordination in children with developmental coordination disorder

Children with developmental coordination disorder (DCD) struggle with the acquisition of coordinated motor skills. This paper adopts a dynamical systems perspective to assess how individual coordination solutions might emerge following an intervention that trained accurate gaze control in a throw and catch task. Kinematic data were collected from six upper body sensors from twenty-one children with DCD, using a 3D motion analysis system, before and after a 4-week training intervention. Covariance matrices between kinematic measures were computed and distances between pairs of covariance matrices calculated using Riemannian geometry. Multidimensional scaling was then used to analyse differences between coordination patterns. The gaze trained group revealed significantly higher total coordination (sum of all the pairwise covariances) following training than a technique-trained control group. While the increase in total coordination also significantly predicted improvement in task performance, the distinct post-intervention coordination patterns for the gaze trained group were not consistent. Additionally, the gaze trained group revealed individual coordination patterns for successful catch attempts that were different from all the coordination patterns before training, whereas the control group did not. Taken together, the results of this interdisciplinary study illustrate how gaze training may encourage the emergence of coordination via self-organization in children with DCD.

Implicit Cognition and Psychopathology: Looking Back and Looking Forward.

Implicit cognitive processing is theorized to have a central role in many forms of psychopathology. In the current review, we focus on implicit associations, by which we mean evaluative representations in memory that are difficult to control and do not require conscious reflection to influence affect, cognition, or behavior. We consider definitional and measurement challenges before examining recent empirical evidence for these associations in anxiety, obsessive-compulsive, posttraumatic stress, depressive, and alcohol use disorders. This examination is framed by a brief review of the ways that prominent models of psychopathology represent biased implicit processing of disorder-relevant information. We consider to what extent models reflect more traditional automatic/implicit versus strategic/explicit dual-process perspectives or reflect more recent dynamical systems perspectives in which mental representations are iteratively reprocessed, evolving continuously. Finally, we consider the future research needed to better understand the interactive and temporal dynamics of implicit cognition in psychopathology.

A dynamical systems approach for pineapple cryopreservation analysis

Abstract The present paper focuses on the cryopreservation process and particularly in the evaluation of the viability of the pineapple apex as a result of the cryopreservation process. Instead of a regeneration measure of the viability we advocate here the use of electrolyte leakage measurements by conductivity and provide a control engineering perspective on this methodology Conductivity measurement considerably reduce the time to evaluate the viability (to the order of days). It will be shown how this technique can be fine-tuned within a model-based approach and bring the viability evaluation to order of hours. The main contribution of the present paper is the analysis of the electrolyte leakage technique in a dynamical systems perspective. Based on the collected data, we construct linear dynamical models for particular survival rates. These models will be subsequently used for the evaluation of cell viability. A particular technical aspect is related to the uncertainty description and the use of the dynamical evolution in the regression analysis of the viability.

Complex Dynamical Systems in Human Development

Researchers from the complex dynamical systems perspective seek their explanations of human behavior and development in the dynamical interactions across many levels in an active, situated individual. Tat is to say, behavior and development are both constraining and constrained by the continuous exchange between a myriad of processes distributed across brain, body, and environment. This fundamentally questions the more traditional rationale that behavior and development of any kind can be explained by targeting a low number of domain-specific, static components or environmental factors. In such a mechanistic approach, components are typically thought to exert their causal effects in a chain-like fashion, and development is explained by the function and place of the components in the chain. However, compiling evidence demonstrates that human behavior and development are dynamic, multi-scaled, and emergent phenomena. It is for this reason that they should be studied from a complex dynamical systems perspective.

Evolutionary Analysis of a Three-Dimensional Carbon Price Dynamic System

The carbon market is the least-cost tool to reduce carbon emissions. This study explores the evolution of the carbon price in the carbon market from a dynamic system perspective. A three-dimensional carbon price dynamic system is established to quantify the interactions among the carbon price, energy price, and economic growth. The system built in this study presents various dynamic characteristics including chaotic attractors and stable equilibria. Specifically, the existence of chaos in the system is verified by Lyapunov exponents spectrum and bifurcation diagram. In contrast, the system tends to be stable in the case of China after identifying the system parameters through the genetic algorithm. Furthermore, evolutionary trends of the carbon price are analyzed when the system parameters are perturbed. The results show that the carbon price is positively correlated with energy price as well as energy price policy. Besides, the level of the carbon price is negatively correlated with government control in the short term and positively correlated in the long term. This study can help analyze trends in the carbon price in the mid-term to long-term.

A Switching Hybrid Dynamical System: Toward Understanding Complex Interpersonal Behavior

Complex human behavior, including interlimb and interpersonal coordination, has been studied from a dynamical system perspective. We review the applications of a dynamical system approach to a sporting activity, which includes continuous, discrete, and switching dynamics. Continuous dynamics identified switching between in- and anti-phase synchronization, controlled by an interpersonal distance of 0.1 m during expert kendo matches, using a relative phase analysis. In the discrete dynamical system, return map analysis was applied to the time series of movements during kendo matches. Offensive and defensive maneuvers were classified as six coordination patterns, that is, attractors and repellers. Furthermore, these attractors and repellers exhibited two discrete states. Then, state transition probabilities were calculated based on the two states, which clarified the coordination patterns and switching behavior. We introduced switching dynamics with temporal inputs to clarify the simple rules underlying the complex behavior corresponding to switching inputs in a striking action as a non-autonomous system. As a result, we determined that the time evolution of the striking action was characterized as fractal-like movement patterns generated by a simple Cantor set rule with rotation. Finally, we propose a switching hybrid dynamics to understand both court-net sports, as strongly coupled interpersonal competition, and weakly coupled sports, such as martial arts.

Ontogenesis of learning and memory: Biopsychosocial and dynamical systems perspectives

In this article, we review recent empirical and theoretical work on infant memory development, highlighting future directions for the field. We consider the state of the field since Carolyn Rovee-Collier's call for developmental scientists to "shift the focus from what to why," emphasizing the function of infant behavior and the value of integrating fractionized, highly specialized subfields. We discuss functional approaches of early learning and memory, including ecological models of memory development and relevant empirical work in human and non-human organisms. Ontogenetic changes in learning and memory occur in developing biological systems, which are embedded in broader socio-cultural contexts with shifting ecological demands that are in part determined by the infants themselves. We incorporate biopsychosocial and dynamical systems perspectives as we analyze the state of the field's integration of multiple areas of specialization to provide more holistic understanding of the contributing factors and underlying mechanisms of the development of memory.