Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 8.6, Problem 1E
Interpretation Introduction

Interpretation:

  • (a) To sketch all the qualitatively different phase portraits arising due to varying parameters -ω1, ω2

  • (b) To find the curves in the parameter space along which the bifurcation occurs.

  • (c) To classify the bifurcations and to draw the stability diagram in the parameter space.

Concept Introduction:

  • ➢ The fixed point of a differential equation is the point where f(x*) = 0 ; while substitution f(x*) = x˙ is used and x&*#x00A0;is a fixed point.

  • ➢ The phase portraits represent the trajectories of the system with respect to the parameters and give a qualitative idea about the evolution of the system, its fixed points, and whether they will attract or repel the flow, etc.

  • ➢ The diagram which shows the different types of behaviours that can occur in the parameter space is called the stability diagram.

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