Ueda

So far I've looked at undriven systems.

The periodically driven Ueda oscillator is described thus [1]:

Here the thing has a sinusoidal driving term on the right hand side. I naïvely thought that this term should be had by integrating 1 volt (actually minus one volt) - to yield t - and then taking the sine of it...but then after some thought I realised that this sinusoidal term can be cooked up more elegantly (and importantly without any limit on t) by solving another differential equation:

 with initial conditions z = 0 and dz/dt = 1. This gives the solution

Scaled equations (by a factor of two).

Patching diagram.

The problem was set up for the parameters used in reference [1], a = 7.5, b = 0.05 and ω = 1. Initial condition was x0 = 2.5.

Below (red plot) is the result (0.2 V/cm horizontal axis (x) and 0.5 V/cm vertical axis (y)). The left hand blue plot is taken from reference [1]:

Reference

[1] Dumitru Deleanu, Description of strange attractors using invariants of phase-plane, Proc. 13th WSEAS Conf. on mathematical methods, computational techniques and intelligent systems, 2011, pp. 113 - 116.