/pdf/dynamical-systems-with-applications-using-maple-6glx3v43l8.pdf

Dynamical Systems with Applications Using MAPLE

Chaotic phenomena and presence of complexity in various nonlinear dynamical systems extensively discussed in the context of recent researches. Discrete as well as continuous dynamical systems both considered here. Visualization of regularity and chaotic motion presented through bifurcation diagrams by varying a parameter of the system while keeping other parameters constant. In the processes, some perfect indicator of regularity and chaos discussed with appropriate examples. Measure of chaos in terms of Lyapunov exponents and that of complexity as increase in topological entropies discussed. The methodology to calculate these explained in details with exciting examples. Regular and chaotic attractors emerging during the study are drawn and analyzed. Correlation dimension, which provides the dimensionality of a chaotic attractor discussed in detail and calculated for different systems. Results obtained presented through graphics and in tabular form. Two techniques of chaos control, pulsive feedback control and asymptotic stability analysis, discussed and applied to control chaotic motion for certain cases. Finally, a brief discussion held for the concluded investigation.

/pdf/chaos-and-complexity-dynamics-of-evolutionary-systems-13gngkkocr.pdf

Chaos and Complexity Dynamics of Evolutionary Systems

In this paper, we have considered Time-Frequency Analysis (TFA) and Poincare Surface of Section (PSS) for the study of the phase space structure of nonlinear dynamical system. We have examined a sample of orbits taken in the framework of Circular Restricted Three-Body Problem (CRTBP). We have computed ridge-plots (i.e. time-frequency landscape) using the phase of the continuous wavelet transform. Clear visualization of resonance trappings and the transitions is an important feature of this method, which is presented using ridge-plots. The identification between periodic and quasi-periodic, chaotic sticky and nonsticky and regular and chaotic orbits are done in comparatively less time and with less computational effort. The spatial case of Circular Restricted Three-Body problem is considered to show the strength of Time-Frequency Analysis to higher dimensional systems. Also, with the help of ridge-plots, we can visualize the phenomenon of transient chaos.

Characterization of the Phase Space Structure of Circular Restricted Three-Body Problem: An Alternative Approach

/pdf/complexity-dynamics-of-gumowski-mira-map-2wm7e0o4q1.pdf

Complexity Dynamics of Gumowski-Mira Map

Complex evolutionary behavior of an age-structured predator-prey threedimensional system has been investigated analytically as well as numerically. Natural populations, whose generations are non-overlapping, can be described by model of difference equations that explains how the populations evolve in discrete time steps. In this paper stability criteria of fixed points of 3-dimentional discrete model are discussed. Bifurcation diagrams of this map are drawn by varying one parameter while fixing value of other parameters. To examine complexity of the map during evolution, certain chaotic measures such as calculations of Lyapunov characteristic exponents (LCEs), topological entropies and correlation dimension have been done and represented graphically.

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L. M. Saha

Papers

Complexities in Age Structured Predator-Prey System