Chapter 6.5, Problem 13E

Interpretation Introduction

Interpretation:

To show that the Duffing equation $\ddot{\text{x}}\text{ + x + ε}{x}^3$ has a non-linear centre at origin for all $\text{ε}$> 0 and to show that for $\text{ε}$< 0 all trajectories near the centre are closed.

Concept Introduction:

Duffing equation models the damped and driven oscillators which do not exactly follow hook’s law.

Trajectories in a phase plane represent the evolution of a system with respect to time and change in parameters.