Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780429972195
Author: Steven H. Strogatz
Publisher: Taylor & Francis
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Chapter 10.6, Problem 1E
Interpretation Introduction

Interpretation:

To plot the sine map for random initial condition.

To find r1, r2, r3, r4, r5, r6 by resolving the diagram and to find Feigenbaum ratio numerically using r1, …., r6.

Concept Introduction:

  • The map is a difference equation which follows xn+1=f(xn).

  • Superstable fixed points are fixed points with multiplier λ= 0. They are called superstablebecauseany disturbances applied to them decay much faster thannon-zero λ terms at an ordinary stable point.

  • The plot of the equation is called asine map when it follows the difference equation -

    xn+1=rsinπxnfor 0 r 1 and 0 x 1.

    The convergence rate of all unimodal maps appears to be constant. This constant is called the Feigenbaum number which is given by, δ= 4.669....

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