scholarly journals Chaotic Dynamics and Complexity in Real and Physical Systems

2021 ◽  
Author(s):  
Mrinal Kanti Das ◽  
Lal Mohan Saha
Keyword(s):  
Complex Dynamics ◽  
Nonlinear Dynamical Systems ◽  
Neuronal Dynamics ◽  
Financial Model ◽  
Nonlinear Dynamical ◽  
Physical Systems ◽  
Investment Demand ◽  
Model Complex ◽  
Artificial Neural Network Ann ◽  
Emergence Of Chaos

Emergence of chaos and complex behavior in real and physical systems has been discussed within the framework of nonlinear dynamical systems. The problems investigated include complexity of Child’s swing dynamics , chaotic neuronal dynamics (FHN model), complex Food-web dynamics, Financial model (involving interest rate, investment demand and price index) etc. Proper numerical simulations have been carried out to unravel the complex dynamics of these systems and significant results obtained are displayed through tables and various plots like bifurcations, attractors, Lyapunov exponents, topological entropies, correlation dimensions, recurrence plots etc. The significance of artificial neural network (ANN) framework for time series generation of some dynamical system is suggested.

scholarly journals Theorems and Application of Local Activity of CNN with Five State Variables and One Port

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Gang Xiong ◽  
Xisong Dong ◽  
Li Xie ◽  
Thomas Yang
Keyword(s):  
Bifurcation Diagram ◽  
Complex Dynamics ◽  
Nonlinear Dynamical Systems ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
State Variables ◽  
Nonlinear Dynamical ◽  
Local Activity ◽  
Homogeneous Lattice ◽  
Coupled Cells

Coupled nonlinear dynamical systems have been widely studied recently. However, the dynamical properties of these systems are difficult to deal with. The local activity of cellular neural network (CNN) has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice, which is composed of coupled cells. In this paper, the analytical criteria for the local activity in reaction-diffusion CNN with five state variables and one port are presented, which consists of four theorems, including a serial of inequalities involving CNN parameters. These theorems can be used for calculating the bifurcation diagram to determine or analyze the emergence of complex dynamic patterns, such as chaos. As a case study, a reaction-diffusion CNN of hepatitis B Virus (HBV) mutation-selection model is analyzed and simulated, the bifurcation diagram is calculated. Using the diagram, numerical simulations of this CNN model provide reasonable explanations of complex mutant phenomena during therapy. Therefore, it is demonstrated that the local activity of CNN provides a practical tool for the complex dynamics study of some coupled nonlinear systems.

scholarly journals Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors

2013 ◽  
Vol 25 (2) ◽  
pp. 328-373 ◽  
Author(s):  
Auke Jan Ijspeert ◽  
Jun Nakanishi ◽  
Heiko Hoffmann ◽  
Peter Pastor ◽  
Stefan Schaal
Keyword(s):  
Motor Control ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Nonlinear Dynamical Systems ◽  
Emergent Behavior ◽  
Nonlinear Dynamical ◽  
Movement Primitives ◽  
Model Complex ◽  
Linear Differential ◽  
Goal Directed Behavior

Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.

scholarly journals NONLINEAR DYNAMICS OF MOVING CURVES AND SURFACES: APPLICATIONS TO PHYSICAL SYSTEMS

2005 ◽  
Vol 15 (01) ◽  
pp. 51-63 ◽  
Author(s):  
S. MURUGESH ◽  
M. LAKSHMANAN
Keyword(s):  
Dynamical Systems ◽  
Soft Matter ◽  
Evolution Equations ◽  
Nonlinear Dynamical Systems ◽  
Dimensional Space ◽  
Classical Mechanics ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Dynamical ◽  
Physical Systems ◽  
Curves And Surfaces

The subject of moving curves (and surfaces) in three-dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a variety of physical problems in different disciplines. Making use of the underlying geometry, one can very often relate the associated evolution equations to many interesting nonlinear evolution equations, including soliton possessing nonlinear dynamical systems. Typical examples include dynamics of filament vortices in ordinary and superfluids, spin systems, phases in classical optics, various systems encountered in physics of soft matter, etc. Such interrelations between geometric evolution and physical systems have yielded considerable insight into the underlying dynamics. We present a succinct tutorial analysis of these developments in this article, and indicate further directions. We also point out how evolution equations for moving surfaces are often intimately related to soliton equations in higher dimensions.

Linear and Nonlinear Dynamic Behaviour

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamic Behavior ◽  
Dynamic Systems ◽  
Dynamic Behaviour ◽  
Nonlinear Dynamical Systems ◽  
Logistic Map ◽  
Nonlinear Dynamical ◽  
Deterministic Dynamic ◽  
Random Behavior ◽  
Single Solution ◽  
Equivalent Systems

In this chapter, we describe how highly erratic dynamic behavior can arise from a nonlinear logistic map, and how this apparently random behavior is governed by a surprising order. With this lesson in mind, we should not be overly surprised that highly erratic and random appearing observed data might also be generated by parsimonious deterministic dynamic systems. At a minimum, we contend that researchers should apply NLTS to test for this possibility. We also introduced tools to analyze dynamic behavior that form the foundation for NLTS. In particular, we have stressed the quite unexpected capability to achieve some form of predictability even with only one trajectory at hand. In subsequent chapters, we treat known nonlinear dynamical systems as unknown, and investigate how NLTS methods rely on a single solution (or multiple solutions) generated by them to reconstruct equivalent systems. This is a conventional approach in the literature for seeing how NLTS methods work since we know what needs to be reconstructed.

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