Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 7.5, Problem 2E
Interpretation Introduction

Interpretation:

To analyze the van der Pol oscillator for μ>>1 in the standard phase plane where x˙ = y and y.=Xμ(X21) and the advantage of Lienard plane.

Concept Introduction:

From the expression of van der pol, the non-linear dynamic equation is x¨ + μx˙(x2-1) + x = 0. Here, x is the position coordinate, and μ is the scalar parameter.

The expression of x¨ and x˙ is x¨ = d2xdt2, x˙ = dxdt.

The Leonhard’s plane is the plane in which the non-linear dynamic equation is shown in the graph of xy plane and in which vector field is vertical. This is called null cline.

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