Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 2.5, Problem 1E
Interpretation Introduction

Interpretation:

The values of c are to be found such that the origin x = 0 is a stable fixed point if a particle travels on the half-line x0 with a velocity given by x˙ = -xc, where c is real and constant. To find how long does it take for the particle to travel from x = 1 to x = 0 if c is chosen such that x = 0 is stable.

Concept Introduction:

Fixed points are the points where x˙ = 0.

If x is the fixed point of the system, then it is stable if x¨ < 0, and the flow is toward the left. It is unstable if x¨ > 0, and the flow is toward the right.

Time taken by the particle can be found by integrating the given equation and substituting the given conditions.

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