Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780429972195
Author: Steven H. Strogatz
Publisher: Taylor & Francis
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Chapter 10.2, Problem 8E
Interpretation Introduction

Interpretation:

Plot orbit diagram for map equation xn+1= r xn-xn3. Also, try different initial conditions

Concept Introduction:

  • ➢ Standard Periodic-doubling: It is a discreet dynamic system equation in which a small change in a parameter value in the system equation changes to the new behavior with double the period of the original system. The appearance of numerous period-doubling cascades is among the most prominent features of parameterized maps, that is, smooth one-parameter families of maps F: R ×MM Here, M is a smooth locally compact manifold without boundary, typically RN, each cascade has infinitely many period-doubling bifurcations, and it is typical to observe that, whenever there are any cascades, there are infinitely many cascades. We develop a general theory of cascades for generic  F.

  • ➢ Logistic map: A logistic map is defined as the polynomial map of the degree two and chaotic behavior can arise from a non-linear dynamic equation.

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