Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 3.5, Problem 8E
Interpretation Introduction

Interpretation:

To show that u˙=au+bu3cu5 can be rewritten as dx = rx + x3 - x5, where a=0.

Concept Introduction:

The supercritical pitchforkis similarlylabelled as forward bifurcation and is closely related to a continuous or second-order phase transition.

In statistical mechanics, the subcritical bifurcation is sometime called inverted or backward bifurcation and is related to discontinuous or first order phase transition.

The given first order system equation is u˙=au+bu3cu5 and has a subcritical pitchfork bifurcation at a=0.

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