Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 5.1, Problem 10E
Interpretation Introduction

Interpretation:

To determine whether the origins of the given systems of differential equations are attracting, Liapunov stable, asymptotically stable or none of these.

Concept Introduction:

Point x* of a system x˙ = f(x) is attracting, if any trajectory that starts within a distance δ of x* isguaranteed to converge to x* eventually.

I.e. x* is attracting, if there is a δ> 0, such that limtx(t) = x*, whenever x(0) - x* < δ.

Point is Liapunov stable, if nearby trajectories remain close for alltime.

I.e. for each ε> 0, there is a δ> 0, such that x(0) - x* < ε, whenever x(0) - x* < δ.

x* isasymptotically stable, if it is both attracting and Liapunov stable.

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