Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 5.2, Problem 12E
Interpretation Introduction

Interpretation:

Write the system equation in two-dimensional linear system. Show that for R>0, the origin is asymptotically stable and it is neutrally stable if R=0. For R2C4L positive, negative, or zero, classify the fixed point at the origin, and plot the phase diagram.

Concept Introduction:

A two dimensional linear system can be expressed in the form as

x˙=ax+byy˙=cx+dy

Here a, b, c, d are parameters. This linear system can be represented in the matrix form as

x˙=Ax

Here the matrix x˙ is represented as

x˙ = [x˙y˙] and A=(abcd)

[x˙y˙]=(abcd)(xy)

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