EBK NONLINEAR DYNAMICS AND CHAOS WITH S
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Chapter 5.1, Problem 11E
Interpretation Introduction

Interpretation:

By using definitions of different types of stabilities, the stabilities of fixed points are to be proved.

Concept Introduction:

A fixed point x*=0 is said to be globally attracting, if x* attracts all trajectories in the phase plane.

Liapunov Stable: A fixed point is Liapunov stable, if all the trajectories start sufficiently close to x* and remains close to it for all positive time.

When a fixed point is Liapunov stable, but not attracting is called neutrally stable. The nearby trajectories are neither attracted nor repelled from neutrally stable points.

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