# Phase Plane Trajectories of the Unforced Duffing Oscillator

Phase Plane Trajectories of the Unforced Duffing Oscillator

This Demonstration allows exploration of phase plane trajectories generated by the unforced Duffing oscillator. This oscillator can be expressed as a system of coupled differential equations given by:

x

t

y

t

3

The initial conditions for the system are selected by using a locator point. Given these initial conditions, a trajectory is generated and plotted over the phase plane vector field. The filled dots correspond to equilibrium points. By varying the time parameter, system parameters, and initial conditions, interesting dynamical evolution in the trajectories can be observed.