Nonlinear Dynamical Systems Theory Research Articles

Skill Acquisition in Physical Education: A Speculative Perspective

How we learn motor skills has always been of interest to physical educators. Contemporary conceptual frameworks about motor skill learning draw from earlier behavioral and cognitive psychology learning theories. As a point of departure this paper foregrounds complexity theorizing, arguing that skill is contingent upon the performer's physical and social context. Drawing on nonlinear dynamics systems theory, ecological psychology (Gibson, 1979), its associated perception/ action coupling (Kugler and Turvey, 1988), an adaption to Gibson's ecological theory (Withagen & van der Kamp, 2010), and the sociological framework of Pierre Bourdieu (1977, 1990, 1998, 2000), it is argued that ecological perspectives and social theories that take account of the complexity of the performance contexts have a part to play in explaining how physical skills are performed and learnt. The relational properties between the learner and the context are essential elements of skill.

Nonlinear Dynamical Systems Theory and Engineering Neural Network : Can Each Afford Plausible Interpretation of 'How' and 'What'?

Nonlinear Dynamical Systems Theory and Engineering Neural Network : Can Each Afford Plausible Interpretation of 'How' and 'What'?

Early dysfunction of functional connectivity in healthy elderly with subjective memory complaints

It is still an open question whether subjective memory complaints (SMC) can actually be considered to be clinically relevant predictors for the development of an objective memory impairment and even dementia. There is growing evidence that suggests that SMC are associated with an increased risk of dementia and with the presence of biological correlates of early Alzheimer's disease. In this paper, in order to shed some light on this issue, we try to discern whether subjects with SMC showed a different profile of functional connectivity compared with subjects with mild cognitive impairment (MCI) and healthy elderly subjects. In the present study, we compare the degree of synchronization of brain signals recorded with magnetoencephalography between three groups of subjects (56 in total): 19 with MCI, 12 with SMC and 25 healthy controls during a memory task. Synchronization likelihood, an index based on the theory of nonlinear dynamical systems, was used to measure functional connectivity. Briefly, results show that subjects with SMC have a very similar pattern of connectivity to control group, but on average, they present a lower synchronization value. These results could indicate that SMC are representing an initial stage with a hypo-synchronization (in comparison with the control group) where the brain system is still not compensating for the failing memory networks, but behaving as controls when compared with the MCI subjects.

Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory

The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension ‘m’ and time delay ‘τ’ when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.

Attractor structures of riftogenesis in the lithosphere of Baikal Rift System

The study results of modern geodynamics and tectonophysics of the lithosphere of Baikal Rift System (BRS) are generalized. By the data on radii of dislocations, three areas of maximal strain-strength anisotropy of the medium are distinguished, while analysis of seismic moments of earthquakes has showed that in these parts of the lithosphere mostly dip-slip fault-causing quakes of various energy classes take place; i.e., riftogenesis processes dominate. Within the framework of the theory of nonlinear dissipative dynamical systems, these areas are classified as attractor structures of riftogenesis (ASR). ASRs are located in the central part and in the flanks of the BRS, and they form nonlinearity and instability of modern geodynamical and tectonophysical processes in the lithosphere, which are manifested in seismicity of the Baikal Region and Mongolia.

Dynamic patterns of flow in the workplace: Characterizing within‐individual variability using a complexity science approach

AbstractAs a result of the growing interest in studying employee well‐being as a complex process that portrays high levels of within‐individual variability and evolves over time, this present study considers the experience of flow in the workplace from a nonlinear dynamical systems approach. Our goal is to offer new ways to move the study of employee well‐being beyond linear approaches. With nonlinear dynamical systems theory as the backdrop, we conducted a longitudinal study using the experience sampling method and qualitative semi‐structured interviews for data collection; 6981 registers of data were collected from a sample of 60 employees. The obtained time series were analyzed using various techniques derived from the nonlinear dynamical systems theory (i.e., recurrence analysis and surrogate data) and multiple correspondence analyses. The results revealed the following: 1) flow in the workplace presents a high degree of within‐individual variability; this variability is characterized as chaotic for most of the cases (75%); 2) high levels of flow are associated with chaos; and 3) different dimensions of the flow experience (e.g., merging of action and awareness) as well as individual (e.g., age) and job characteristics (e.g., job tenure) are associated with the emergence of different dynamic patterns (chaotic, linear and random). Copyright © 2011 John Wiley & Sons, Ltd.

Commentary on Paper by Terry Marks-Tarlow

This discussion of the paper merging and emerging: A nonlinear portrait of intersubjectivity during psychotherapy focuses on how the original paper demonstrates the usefulness of the concepts of nonlinear dynamics systems theory (NLD) to clinical psychoanalysis. Diagnosis conceptualize in NLD terms successfully resists the pressure to reduce complex situations to overly simple few word phrases. The phenomena of transference and repetition are redescribed as resulting from an iterative process that is evident in complex adaptive systems. The model of psychoanalysis in terms of coupled oscillators is demonstrated to be clinically useful as is the concept of emergence which overcomes some of the less useful aspects of the reductionist program. The idea of studying boundaries per se, as opposed to their function of separating individuals, arises naturally from the study of fractals and promises to clarify the oversimplified discussions of these matters in the psychoanalytic literature. The original author has successfully demonstrated how useful NLD conceptualizations can be to the clinical psychoanalyst.

Research on Railway Engineering Cost Prediction Model Based on Chaotic Neural Networks and CS

It is always hard to draw on the experience of completed projects to predict engineering cost, and the nonlinear characteristic of the influence factors of engineering cost increases the difficulty of prediction. Less efforts and higher accuracy are the objects pursued by related researchers. In this paper, the Cost Significant theorem is applied to simplify computing and the chaotic neural network is used to improve accuracy. The prediction model is rooted from the nonlinear dynamic chaotic system theory and two techniques employed are phase space reconstruction and chaotic neural network construction. The experiment results indicate that the model is suitable for estimating short-term engineering investment and the prediction accuracy is improved.

Coping with stress through decisional control: Quantification of negotiating the environment

Coping with stress through 'decisional control' - positioning oneself in a multifaceted stressing situation so as to minimize the likelihood of an untoward event - is modelled within a tree-structure scenario, whose architecture hierarchically nests elements of varying threat. Analytic and simulation platforms quantify the game-like interplay of cognitive demands and threat reduction. When elements of uncertainty enter the theoretical structure, specifically at more subordinate levels of the hierarchy, the mathematical expectation of threat is particularly exacerbated. As quantified in this model, the exercise of decisional control is demonstrably related to reduction in expected threat (the minimum correlation across comprehensive parameter settings being .55). Disclosure of otherwise intractable stress-coping subtleties, endowed by the quantitative translation of verbal premises, is underscored. Formalization of decisional stress control is seen to usher in linkages to augmenting formal developments from fields of cognitive science, preference and choice modelling, and nonlinear dynamical systems theory. Model-prescribed empirical consequences are stipulated.

On partial stability theory of nonlinear dynamic systems

A stability problem with respect to a part of variables of the zero equilibrium position is considered for nonlinear non-stationary systems of ordinary differential equations with the continuous right-hand side. As compared to known assumptions, more general assumptions are made on the initial values of variables non-controlled in the course of studying stability. In addition, a stability problem is considered with respect to a part of variables of the "partial" equilibrium position, with similar assumptions made for initial values of variables that do not define the given equilibrium position. Conditions of stability and asymptotic stability of this type are obtained within the method of Lyapunov functions and generalize a number of existing results. The results are applied to the stability problem with respect to a part of variables of equilibrium positions of nonlinear holonomic mechanical systems. The problem of unification (to a certain extent) of the process of studying partial stability problems of stationary and non-stationary systems is discussed.

Functional Connectivity in Mild Cognitive Impairment During a Memory Task: Implications for the Disconnection Hypothesis

Mild cognitive impairment (MCI) has been considered an intermediate state between healthy aging and dementia. The early damage in anatomical connectivity and progressive loss of synapses that characterize early Alzheimer's disease suggest that MCI could also be a disconnection syndrome. Here, we compare the degree of synchronization of brain signals recorded with magnetoencephalography from patients (22) with MCI with that of healthy controls (19) during a memory task. Synchronization Likelihood, an index based on the theory of nonlinear dynamical systems, was used to measure functional connectivity. During the memory task patients showed higher interhemispheric synchronization than healthy controls between left and right -anterior temporo-frontal regions (in all studied frequency bands) and in posterior regions in the γ band. On the other hand, the connectivity pattern from healthy controls indicated two clusters of higher synchronization, one among left temporal sensors and another one among central channels. Both of them were found in all frequency bands. In the γ band, controls showed higher Synchronization Likelihood values than MCI patients between central-posterior and frontal-posterior channels and a high synchronization in posterior regions. The inter-hemispheric increased synchronization values could reflect a compensatory mechanism for the lack of efficiency of the memory networks in MCI patients. Therefore, these connectivity profiles support only partially the idea of MCI as a disconnection syndrome, as patients showed increased long distance inter-hemispheric connections but a decrease in antero-posterior functional connectivity.

To Speak or Not to Speak—The Taboo of Communication

In this discussion, Dr. William Lubart's case presentation is discussed from two complementary points of view—nonlinear dynamic systems theory and the “taboo of communication.” The therapeutic couple is considered as a unitary system (the “analytic unity”), and the developmental trajectory of this particular process is discussed with an emphasis on choice points depending on whether painful subjects are spoken about openly or shrouded in silence. Brief consideration is given as to whether greater efforts to break the taboo around communication might have altered the life of this particular analytic unity. The importance of the struggle to find ways to speak about what is happening is highlighted, especially with difficult, shameful, and painful subjects that are ordinarily taboo.

A Human Family: Commentary on Paper by Elisabeth Fivaz-Depeursinge, Chloé Lavanchy-Scaiola, and Nicolas Favez

In discussing the paradigm shifting work of Fivaz-Depeursinge and her colleagues, I illustrate how developmental conceptions have shifted from a narrative centered on the discovery of “an Other” to narratives emphasizing what these authors term “collective intersubjectivity.” In this latter view, humans simultaneously share affect and intention with multiple others from birth, and subsequently continue to develop increasingly sophisticated means for doing so thorough out their lives. I situate this phenomenon in philosophy, nonlinear dynamic systems theory and evolutionary biology in order to highlight the species specific, phenomenologically given, and ecologically situated aspects of our intersubjective condition. Intersubjectivity from the perspective of Fivaz-Depeursinge and her group opens us to this collective dimension of membership in a human family.

The rich structure of transition in a shear flow

Significant advances have been made in applying ideas from nonlinear dynamical systems theory to flows which exhibit sequences of bifurcations in the transition to turbulence. Moreover, the recent discoveries of finite-amplitude states in linearly stable flows holds great promise for a breakthrough in our understanding transition in shear flows. Tsukahara, Tillmark & Alfredsson (J. Fluid Mech., 2010, this issue, vol. 648, pp. 5–33) study a novel variant of a classical shear flow by adding global rotation. The competition between the induced body force and shear-induced instabilities leads to the discovery of a rich and beautiful tapestry of transition sequences.

Catastrophes and Chaos in Business Cycle Theory

The primary thesis of this paper is that a nonlinear dynamical systems theory provides a basis for conducting all kinds of comparisons in the theory of business cycles, and it also enables its further development. A cognitive aim was to show that applying the theory of bifurcations and morphogenesis in the domain of economic fluctuations allows us to construct models of the cycle with greater explicatory and utility values than there were so far. In this way, the precision and consistency of the theory increases. In this field, applications of catastrophe theory are of great importance. Another fact was indicated, namely the theory of deterministic chaos places the issues of explanation and forecasting in economics in a totally dierent light. It turns out that we are dealing with at least three sources of complexity in economic systems: chaotic attractors, invariant chaotic sets that are not attracting in the form of chaotic saddles and the eects of fractal basin boundaries. This, in turn, limits the eectiveness of traditional economic policy. Economic management should be based on procedures that lower complexity of economic systems, however sometimes lower complexity incurs bigger instability. The paper is a survey of applications of nonlinear dynamical systems to mathematical business cycle models. The survey encompasses both earlier models that were built in 1970s, as well as later concepts. The paper also features a few of my newest results of numerical studies of some nonlinear economic systems.

Nonlinear Dynamics of Team Performance and Adaptability in Emergency Response

The impact of team size and performance feedback on adaptation levels and performance of emergency response (ER) teams was examined to introduce a metric for quantifying adaptation levels based on nonlinear dynamical systems (NDS) theory. NDS principles appear in reports surrounding Hurricane Katrina, earthquakes, floods, a disease epidemic, and the Southeast Asian tsunami. They are also intrinsic to coordination within teams, adaptation levels, and performance in dynamic decision processes. Performance was measured in a dynamic decision task in which ER teams of different sizes worked against an attacker who was trying to destroy a city (total N = 225 undergraduates). The complexity of teams' and attackers' adaptation strategies and the role of the opponents' performance were assessed by nonlinear regression analysis. An optimal group size for team performance was identified. Teams were more readily influenced by the attackers' performance than vice versa. The adaptive capabilities of attackers and teams were impaired by their opponents in some conditions. ER teams should be large enough to contribute a critical mass of ideas but not so large that coordination would be compromised. ER teams used self-organized strategies that could have been more adaptive, whereas attackers used chaotic strategies. The model and results are applicable to ER processes or training maneuvers involving dynamic decisions but could be limited to nonhierarchical groups.

Analytical formulae for predicting the surf-riding threshold for a ship in following seas

Making use of Melnikov’s method, a generalized formula for predicting the surf-riding threshold is developed as an extension to the applications of Kan and Spyrou. A new analytical formula for calculating the surf-riding threshold of a ship in following seas is also proposed in light of nonlinear dynamical system theory. By applying a continuous piecewise linear approximation to the wave-induced surge force, a heteroclinic bifurcation point is obtained analytically with an uncoupled surge equation. Results calculated using these formulae are presented, and they show good agreement with those obtained utilizing numerical bifurcation analysis. Further, it was confirmed that the surf-riding threshold obtained using the proposed formulae agrees reasonably well with that obtained experimentally for an unconventional vessel.

A Mathematica Implementation of Nonlinear Dynamical Systems Theory via the Spider Algorithm and Finding Critical Zeros of High-Degree Polynomials

Important properties pertaining to families of discrete dynamical systems are furnished here by studying the kneading theory developed by Milnor and Thurston, and subsequently implementing the spider algorithm, developed by Hubbard and Schleicher. The focus is on identifying crucial combinatorial and numerical properties of periodic critical orbits in one-dimensional discrete dynamical systems, which are generated by iterating real quadratic polynomial maps that constitute an important class of unimodal systems.

Adaptive synchronisation of fractional-order chaotic systems

A new stability theory of nonlinear dynamic systems is proposed, and a novel adaptive synchronisation method is presented for fractional-order chaotic and hyperchaotic systems based on the theory described in this paper. In comparison with previous methods, not only is the present control scheme simple but also it employs only one control strength, converges very fast, and it is also suitable for a large class of fractional-order chaotic and hyperchaotic systems. Moreover, this scheme is analytical and simple to implement in practice. Numerical and circuit simulations are used to validate and demonstrate the effectiveness of the method.

Increasing the Potassium Channel Density in Regularly Spiking Pyramidal Cells can Turn them into Fast Spiking

The threshold dynamic of neurons can be classified into two main types: regular spiking neurons, showing a continuous frequency-stimulation current relationship and thus an arbitrarily low frequency at threshold current, and fast spiking neurons, showing a discontinuous relationship and a minimum frequency for repetitive firing. In a previous investigation of a hippocampal neuron model, we showed that the membrane density of critical ion channels is important for the bifurcation type and consequently for the threshold dynamics; it can cause the model to switch between fast and regular spiking. In the present study we extend our previous analysis with experimental tests, using the dynamic clamp technique. We injected currents, calculated from voltage clamp descriptions of potassium currents, into regularly spiking pyramidal cells, thereby altering their threshold dynamics to fast spiking. The results confirm the conclusion from the previous study that the type of threshold dynamics of neurons can critically depend on the channel density. Moreover, we show by analysing other well-described membrane models with techniques from nonlinear dynamical system theory how the channel density as bifurcation parameter is influenced by other parameters such as channel kinetics, in some cases reducing the threshold dynamics exclusively to fast spiking. In conclusion, the overall structure of the phase space around the stationary potentials must be taken into account when trying to understand the threshold dynamics of neurons, and, consequently, the global oscillatory activity of networks of neurons.