Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 8.1, Problem 6E
Interpretation Introduction

Interpretation:

Consider the system x˙ = y- 2x, y˙ = μ + x2- y

Sketch the nullclines.

The bifurcations that occur as μ varies is to be found and classified.

The phase portrait as a function of μ is to be sketched.

Concept Introduction:

Geometrically, the x-nullclines are a set of points in the phase plane where vectors are going up or down. Algebraically, they can be found by using f(x,y) = 0.

Geometrically, the y-nullclines are a set of points in the phase plane where vectors are horizontal, going either left or to the right.

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