 # A Chaotic Circuit

### Analysis of a simple electric circuit that displays chaotic behavior

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.

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This substitutes values for parameters into the equations.

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

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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 Mathematica      May 4, 2002