Nonlinear Dynamical Systems Theory Research Articles

Emerging Adulthood and Nonlinear Dynamic Systems Theory

ABSTRACTThe papers in this section on emerging adulthood exemplify the continuous interaction of the cultural surround, biology, and psychology that support a nonlinear dynamic system of development. People in their twenties move through this developmental period in individualized ways, and their ability to successfully traverse these years to adulthood can be helped or hindered by the complex interplay of their individual psychology, environment, and culture.

Dynamic models of large-scale brain activity.

Movement, cognition and perception arise from the collective activity of neurons within cortical circuits and across large-scale systems of the brain. While the causes of single neuron spikes have been understood for decades, the processes that support collective neural behavior in large-scale cortical systems are less clear and have been at times the subject of contention. Modeling large-scale brain activity with nonlinear dynamical systems theory allows the integration of experimental data from multiple modalities into a common framework that facilitates prediction, testing and possible refutation. This work reviews the core assumptions that underlie this computational approach, the methodological framework that fosters the translation of theory into the laboratory, and the emerging body of supporting evidence. While substantial challenges remain, evidence supports the view that collective, nonlinear dynamics are central to adaptive cortical activity. Likewise, aberrant dynamic processes appear to underlie a number of brain disorders.

Ion temperature effects on its chaotic behavior in ion-sheath

Nonlinear dynamical behavior of an ion with finite temperature in a driven plasma ion-sheath has been studied by a numerical solution of fluid equations. Using the concepts of the nonlinear dynamical system theory, the conditions under which the dynamical behavior of the ion becomes chaotic have been investigated. The numerical results have revealed that there is an order-chaos-order transition in the isothermal plasma ion-sheath due to the external oscillating electric field. In the case of an adiabatic ion-sheath, even with a strong external electric field, no chaotic motion has appeared.

Holistic Thinking and Therapeutic Action: Building on Louis Sander’s Contribution

This paper makes the case for a holistic approach to conceptualizing what we actually do with our patients. Psychoanalytic theories, whether comprehensive or circumscribed, conceptualize the nature of analytic interaction and the principles of therapeutic action into distinct theoretical categories. These categories then shape our thinking, causing us to lose sight of our fundamental purpose: to provide each patient with the specific and unique forms of help they need to move toward and achieve their therapeutic aims, both implicit and explicit. To counteract this long-standing trend, we need more holistic constructs oriented toward each patient’s unique, and uniquely complex, aims and process. Louis Sander’s principles of specificity of recognition, specificity of connection, moments of meeting, and progressive fittedness are identified as powerful examples of such higher order constructs. Sander’s language is unique in that it bridges the objective-descriptive perspective of nonlinear dynamic systems theory and the phenomenological perspective of the analytic therapist-at-work. The author adds three of his own concepts to Sander’s, then presents an extended clinical example illustrating the more personal, intuitive, improvisational quality of an analytic process grounded in these principles. The case and discussion follow the evolution of the treatment over time, focusing especially on an extended “moment of meeting” at the conclusion of which the analytic system had reorganized at a dramatically more complex and alive level of relational fittedness.

Dynamical System Analysis of Interacting Hessence Dark Energy inf(T)Gravity

We have carried out dynamical system analysis of hessence field coupling with dark matter inf(T)gravity. We have analysed the critical points due to autonomous system. The resulting autonomous system is nonlinear. So, we have applied the theory of nonlinear dynamical system. We have noticed that very few papers are devoted to this kind of study. Maximum works in literature are done treating the dynamical system as done in linear dynamical analysis, which are unable to predict correct evolution. Our work is totally different from those kinds of works. We have used nonlinear dynamical system theory, developed till date, in our analysis. This approach gives totally different stable solutions, in contrast to what the linear analysis would have predicted. We have discussed the stability analysis in detail due to exponential potential through computational method in tabular form and analysed the evolution of the universe. Some plots are drawn to investigate the behaviour of the system(this plotting technique is different from usual phase plot and that devised by us). Interestingly, the analysis shows that the universe may resemble the “cosmological constant” like evolution (i.e.,ΛCDM model is a subset of the solution set). Also, all the fixed points of our model are able to avoid Big Rip singularity.

First order homogeneous dynamical systems 1: theoretical formulation

Of late, the attention of the dynamicists has increasingly been focused on the multi-degree of freedom (MDOF) nonlinear dynamical systems. In the present paper, a new class of conservative two-DOF nonlinear dynamical systems - first order homogeneous dynamical (FOHD) systems - has been proposed. This investigation is motivated by two-DOF cracked concrete beams undergoing small deformations. For these mechanical systems, the nodal forces are functions homogeneous of order one of the nodal displacements and vice-versa. Under assumptions of lumped nodal masses and classical damping, the equations of motion have been derived in the paper. The nodal displacement space has been partitioned into four elastically-distinct regions. Within the two nonlinear elastic regions, the stiffness and damping coefficients as well as the modal frequencies have been shown to vary continuously but remain constant within the two linear regions. Peculiar characteristics distinguishing the FOHD systems from other known MDOF nonlinear dynamical systems have been identified. Theoretical significance of the proposed FOHD systems in the general nonlinear dynamical systems theory has been brought out. The issues such as empirical validation of the predicted dynamical response and the practical relevance of the work done for the concrete beams under working loads have also been discussed.

Nonlinear dynamical systems seen through the scope of the Quasi-polynomial theory


 A unified theory of nonlinear dynamical systems is presented. The unification relies on the Quasi-polynomial approach of these systems. The main result of this approach is that most nonlinear dynamical systems can be exactly transformed to a unique format, the Lotka-Volterra system. An abstract Lie algebraic structure underlying most nonlinear dynamical systems is found. This structure, based on two sets of operators obeying specific commutation rules and on a Hamiltonian expressed in terms of these operators, bears a strong similarity with the fundamental algebra of quantum physics. From these properties, two forms of the exact general solution can be constructed for all Lotka-Volterra systems. One of them corresponds to a Taylor series in power of time. In contrast with other Taylor series solutions methods for nonlinear dynamical systems, our approach provides the exact analytic form of the general coefficient of that series. The second form of the solution is given in terms of a path integral. These solutions can be transformed back to solutions of the general nonlinear dynamical systems.

Controlling the Temporal Pulse Shape of the Passively Q-Switched Laser by Nonlinear Feedback Control

The design of a nonlinear controller that automatically adjusts the pump rate of the Q-switched laser to allow for customizing the temporal pulse shape of the laser output is proposed. The design is based on a method called feedback linearization, which is a well established technique in nonlinear dynamical system theory. It is demonstrated that such a nonlinear dynamical system can be transformed into a chain of two integrators by applying state feedback. Thus the desired output pulse shape is produced by applying its second derivative to the controller input. The design is verified by simulating the closed loop device in MATLAB Simulink.

Integrative synchronization mechanisms in connectionist cognitive neuroarchitectures

Based on the mathematics of nonlinear Dynamical System Theory, neurocognition can be analyzed by convergent fluid and transient neurodynamics in abstract n-dimensional system phase spaces in the form of nonlinear vector fields, vector streams or vector flows (the so-called “vectorial form”). This processual or dynamical perspective on cognition, including the dynamical binding mechanisms in cognitive neuroarchitectures, has the advantage of a more accurately modeling of the transient cognitive processes. Thus, neurocognition can be considered as being organized by integrative synchronization mechanisms which best explain the liquid flow of neurocognitive information orchestrated in a network of positive and/or negative feedback loops in the subcortical and cortical areas. The human neurocognitive system can be regarded as a nonlinear, dynamical and open nonequilibrium system. This new fluid or liquid perspective in cognitive science and cognitive neuroscience can be regarded as a contribution towards bridging the gap between the discrete, abstract symbolic description of propositions in the mind, and their continuous, numerical implementation in self-organizing neural networks modelling the neural information processing in the human brain.

The Self As a Complex Adaptive System Part III: A Revised View of Development

ABSTRACTThe goal of this project has been to explore the characteristics of the self as a complex adaptive system. It began with the effort to provide a foundation for a developmental theory based on principles from self psychology that also permitted the incorporation of some of the recent findings from neuroscience. Part I (Palombo, 2013a) outlined some features of nonlinear dynamic systems theory and complexity science that provided the basis for a critique of traditional psychodynamic developmental theories. This critique was followed in Part II (Palombo, 2013b) with the proposal of a levels-of-analysis perspective as a methodology to organize the data on development, the three levels of analysis being the neuropsychological, the introspective, and the interpersonal. This article, Part III, outlines the trends that contributed to the revised view of development and proposes a set of processes that are consistent with a nonlinear dynamic perspective that govern human beings' mental activities during development. These processes are the progression from lower to higher levels of complexity, the movement from lesser to greater differentiation, and advancement from lesser to greater individuation.

Nonlinear dynamical systems for theory and research in ergonomics

Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system.Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.

A Discussion of “Disorders of Temporality and The Subjective Experience of Time: Unresponsive Objects and the Vacuity of the Future” by Stephen Seligman

In this review of Stephen Seligman’s contribution to the literature on disorders of temporality, the patient’s ordinary and extraordinary experiences of time in the clinical situation, the reviewer provides both theoretical confirmation and clinical illustration in support of the author’s arguments. Infant research, nonlinear dynamic systems theory, and especially a brain-based psychoanalytic perspective taken from the work of Gerald Edelman are introduced to facilitate understanding of memory in general and the second of Seligman’s disorders of temporality in particular. Edelman’s formulation on the biological evolution of consciousness affords a means to comprehend how the phenomenon of dissociation emerges spontaneously in the clinical situation that matches and offers an explanation Seligman’s own understanding.

Einstein’s Dark Energy via Similarity Equivalence, ‘tHooft Dimensional Regularization and Lie Symmetry Groups

Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv2 leads to Einstein’s celebrated maximal energy equation E = mc2 and how in turn this can be dissected into the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) of the cosmos where m is the mass; v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.

Major fire spread in a tunnel with water mist: A theoretical model

A model of the effect of water mist on major fire spread in a tunnel is described. It employs the concepts of non-linear dynamical systems theory and identifies the onset of instability with major fire spread in a tunnel. The purpose is to identify the thermo-physical and geometrical conditions which lead to instability and sudden fire spread. It uses as a starting point one of the non-linear models for major fire spread which have been developed by the author over many years and assumes that a water mist system operates.The case considered assumes the existence of a longitudinal forced ventilation and predicts the critical heat release rate needed for a fire to spread from an initial fire to an item with a given assumed shape; in the presence of water mist. There is assumed to be no flame impingement on the target object. The target object may be taken to approximate a vehicle. The illustrative case approximating fire spread from an initial fire to a heavy goods vehicle (HGV) is presented; it is not restricted to this case, however. The model is being identified with the name FIRE-SPRINT C1, which is an acronym of Fire Spread in Tunnels, Model C, Version 1. It has been developed from an earlier model, FIRE-SPRINT A3 and considers a case where, in the absence of a fire fighting system, there is the potential for a major fire.

Bubble nonlinear dynamics and stimulated scattering process**Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).

A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller–Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition.

Efficient word reading: Automaticity of print-related skills indexed by rapid automatized naming through cusp-catastrophe modeling

ABSTRACTThe study explored the moderating role of rapid automatized naming (RAN) in reading achievement through a cusp-catastrophe model grounded on nonlinear dynamic systems theory. Data were obtained from a community sample of 496 second through fourth graders who were followed longitudinally over 2 years and split into 2 random subsamples (validation and cross-validation groups). Results verified the superiority of the cusp-catastrophe over linear and logistic models and established RAN-digits performance as a significant bifurcation factor in both concurrent and longitudinal prediction models. These findings suggested that reduced serial naming speed below a critical level was associated with significantly reduced predictability of word reading efficiency from pseudoword decoding ability. Results were tentatively interpreted as documenting the importance of highly automatized coordination of reading-related component processes, indexed by RAN performance, for word reading efficiency during the early and middle stages of reading acquisition.

Causality in Psychiatry: A Hybrid Symptom Network Construct Model.

Causality or etiology in psychiatry is marked by standard biomedical, reductionistic models (symptoms reflect the construct involved) that inform approaches to nosology, or classification, such as in the DSM-5 [Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition; (1)]. However, network approaches to symptom interaction [i.e., symptoms are formative of the construct; e.g., (2), for posttraumatic stress disorder (PTSD)] are being developed that speak to bottom-up processes in mental disorder, in contrast to the typical top-down psychological construct approach. The present article presents a hybrid top-down, bottom-up model of the relationship between symptoms and mental disorder, viewing symptom expression and their causal complex as a reciprocally dynamic system with multiple levels, from lower-order symptoms in interaction to higher-order constructs affecting them. The hybrid model hinges on good understanding of systems theory in which it is embedded, so that the article reviews in depth non-linear dynamical systems theory (NLDST). The article applies the concept of emergent circular causality (3) to symptom development, as well. Conclusions consider that symptoms vary over several dimensions, including: subjectivity; objectivity; conscious motivation effort; and unconscious influences, and the degree to which individual (e.g., meaning) and universal (e.g., causal) processes are involved. The opposition between science and skepticism is a complex one that the article addresses in final comments.

New Developments in Fault Analysis Based on Dynamical Perspective

ABSTRACTElectric power system essentially belongs to strongly nonlinear complex dynamic system. It has strong coupling and other various dynamic characteristics. In theory, the nonlinear dynamical model associated with complex power system should exist. In this paper, we have discussed two kinds of nonlinear circuits, nonlinear RLC circuit that can be constructed to be Liénard equation model and Chua's circuit. In our research, the superstable periodic parameters of period doubling bifurcations are solved accurately, and it is also the fault characteristic in nonlinear circuits, which may represent the essential attribute of complex electric power system. The research will contribute to solving the blackout problems in real electrical engineering. It is an inevitable request that applying nonlinear dynamical system theory to the research of complex electric power system, which is not only beneficial to the effective solution of power system's own problems, but realizing new breakthroughs in nonlinear dynamical system theory by finding new problems.

Multiple-Input Multiple-Output Optical Integrator Design by Non-Interacting Control via Dynamic Extension

The design of a multiple-input multiple-output optical integrator using a semiconductor optical amplifier is proposed. The design is based on non-interacting state feedback control through dynamic extension, which is a well established technique in nonlinear dynamical system theory. First it is shown the dynamical equations of a semiconductor optical amplifier with two inputs and two outputs has a well-defined vector relative degree of [1,1] in a large range of operating points. It is demonstrated that such a device can be transformed into an integrator by applying state feedback. The design is verified by simulating the closed loop device in MATLAB Simulink.

Coherent water transport across the South Atlantic

AbstractThe role of mesoscale eddies in transporting Agulhas leakage is investigated using a recent technique from nonlinear dynamical systems theory applied on geostrophic currents inferred from the over two decade long satellite altimetry record. Eddies are found to acquire material coherence away from the Agulhas retroflection, near the Walvis Ridge in the South Atlantic. Yearly, one to four coherent material eddies are detected with diameters ranging from 40 to 280 km. A total of 23 eddy cores of about 50 km in diameter and with at least 30% of their contents traceable into the Indian Ocean were found to travel across the subtropical gyre with minor filamentation. Only one eddy core was found to pour its contents on the North Brazil Current. While the ability of eddies to carry Agulhas leakage northwestward across the South Atlantic is supported by our analysis, this is more restricted than suggested by earlier ring transport assessments.