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 6E
Interpretation Introduction

Interpretation:

To show that the study state amplitude A(t) dependent on ε according to the power law A*εβ, where β = 0.50 ± 0.01 in context the equation τA˙ = εA - gA3. Determine the landau equation prediction. Find the relation between A* and ε for the equation τA˙ = εA - gA3-kA5, when g = 0. Sketch the bifurcation diagram of A* vs ε for the equation τA˙ = h + εA - gA3-kA5 in the cases g > 0, g = 0 and g < 0. Explain why the given curve has a strange shape.

Concept Introduction:

Express the equation in dimension less form using dimensionless parameter.

Analyze the fixed points for Landau equation and its prediction.

Draw the bifurcation diagram for various conditions.

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