Chaos and Complexity Dynamics of Evolutionary Systems
TLDR
Two techniques of chaos control, pulsive feedback control and asymptotic stability analysis, discussed and applied to control chaotic motion for certain cases and results obtained presented through graphics and in tabular form.Abstract:
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.read more
Citations
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Journal ArticleDOI
Does God play dice?, by Ian Stewart. Pp 317. £15. 1989. ISBN 0-631-16847-8 (Basil Blackwell)
Journal ArticleDOI
An introduction to chaotic dynamical systems
TL;DR: An introduction to chaotic dynamical systems by is just one of the best seller books on the planet? Have you had it? Never? Foolish of you. Now, never ever miss it.
Journal ArticleDOI
An introduction to chaotic dynamical systems (2nd edition), by Robert L. Devaney. Pp 336. £34·95. 1989. ISBN 0-201-13046-7 (Addison-Wesley)
TL;DR: In this paper, the quadratic family has been used to define hyperbolicity in linear algebra and advanced calculus, including the Julia set and the Mandelbrot set.
Book
Introduction to chaos : physics and mathematics of chaotic phenomena
TL;DR: In this paper, the authors describe the characteristics of chaos in nature, including topological entropy, Lyapunov number, and the number of periodic orbits in a topological system.
References
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