Here is a simple circuit containing a sinusoidal voltage source, a resistor, inductor and diode. The presence of the diode introduces nonlinearity and allows for the possibility of complex behavior.

We model the diode as having a piecewise–linear capacitance with a small offset voltage.

The equations for the charge and current in the diode can be written directly in *Mathematica*.

This substitutes values for parameters into the equations.

It is possible to solve the equations by using the *Mathematica* function NDSolve.

Here are the solutions for the charge as a function of time for three values of the driving voltage ÷….

Here are the parametric plots of the charge versus current for the same three values of the driving voltage ÷….

This draws a bifurcation diagram showing how the oscillations of the charge first period double, then eventually become chaotic as the driving voltage increases.

Converted by