Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 3.6, Problem 2E
Interpretation Introduction

Interpretation:

To find the effect of h on bifurcation diagram, where h is the imperfection parameter.

Plot the bifurcation diagram for x˙ = h + rx - x2, for h < 0, h = 0 and h > 0. Also sketch regions in the (r, h) plane that correspond to qualitative different vector fields. Identify the bifurcation that occurs on the boundaries of those regions. Also plot the potential V(x) corresponding to all different regions.

Concept Introduction:

General expression of the imperfect bifurcation system is x˙ = h + rx - f(x).

Here, x is the position, h is the imperfection parameter. and r is a constant parameter.

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