Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780429972195
Author: Steven H. Strogatz
Publisher: Taylor & Francis
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Chapter 3.4, Problem 2E
Interpretation Introduction

Interpretation:

As r varies, the vector fields also varies which are as shown below for the function x˙=rx-sinh(x). The pitchfork bifurcation occurs at a critical value of r and also sketched the bifurcation diagram.

Concept Introduction:

Bifurcation theory is used to study the stability of the dynamical systems.

A pitchfork bifurcation is a bifurcation where the system transitions from one fixed point to three fixed points. Small blank dot is used for unstable point and a black dot represents that at that point, the system is stable.

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