Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 8.4, Problem 12E
Interpretation Introduction

Interpretation:

The period of a closed orbit as a homoclinic bifurcation is approached is to be found by finding the time requires for a trajectory passing through (μ,1) to escape from the saddle for a system x˙μx,y˙=-λsy is x(t)1.

Concept Introduction:

  • ➢ The solution of a system of two simultaneous first-order differential equations, if its matrix has two distinct real eigenvalues, is

    x(t)=C1k1eλ1t and y(t)=C2k2eλ2t, where λ1,λ2 are eigenvalues and k1,k2 are eigen vectors.

  • ➢ A limit cycle is a closed, isolated trajectory. A homoclinic bifurcation occurs when a limit cycle moves closer and closer to a saddle point.

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