Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 2.4, Problem 4E
Interpretation Introduction

Interpretation:

Fixed points of the system x˙ = x2(6 - x) are to be classified using linear stability analysis, and if it fails, by using graphical argument.

Concept Introduction:

Fixed points of a system are the points where x˙ = 0, and are denoted by x

When f '(x)<0, the fixed point is stable.

When f '(x)>0, the fixed point is unstable.

The stability of the fixed point can’t be determined by linear analysisif f '(x)=0, and graphical argument should be used.

Semi stable points are the points at which the local flow is towards them as well as away from them.

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