The van der Pol System

Part 3: Other Nonlinear Systems (Optional)

In your differential system, replace the voltage drop at the semiconductor by I(I³-a). Then redraw your phase plots and solution curves, and answer the following questions.

1. How do the trajectories and solutions change as a varies from 0 to relatively large positive values?
2. What is the nature of the equilibrium point at the origin?
3. Is there always a limit cycle? Is there ever a limit cycle? If there is (at least sometimes) a limit cycle, how does it change as the parameter a changes?

Now repeat steps 1, 2, and 3 with semiconductor voltage drop I(I⁴-a).