Chapter 6.5, Problem 11E

Interpretation Introduction

Interpretation:

Basin of attraction for the system $\dot{\text{x}}\text{ = y}$, ${\dot{\text{y}}\text{ = - by + x - x}}^{\text{3}}$ is to be sketched.

Concept Introduction:

Basin of attraction is the set of initial conditions ${\text{ x}}_0$ such that $\text{ x(t)}\to {\text{x}}^{*}\text{ as t}\to \infty .$

Basin is separated by basin boundary which is stable manifold.

The trajectories comprising stable manifold are known as separatrices.

Basins and their boundaries divide phase space into regions of different long-term behavior.