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 3E
Interpretation Introduction

Interpretation:

The given equationis to be fixedfora finite time x(t)±, where r > 0

Concept Introduction:

By using the concept of existence and uniqueness the solution of the given equation x˙ = rx+x3 where r > 0, is found out.

The existence and uniqueness theorem says that, ‘f(x), and f'(x) are continuous on an open interval R of the x-axis, and suppose that  x0 is a point in R. Then the initial value problem has a solution x(t) on some time interval (-t,t) about t = 0, and the solution is unique’.

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