(Extended, open-ended problem) The second order, nonlinear, ordinary differential equation
![615_33a97ed7-715d-43d2-9a52-93c0dc428d6b.png](https://secure.tutorsglobe.com/CMSImages/615_33a97ed7-715d-43d2-9a52-93c0dc428d6b.png)
governs the oscillations of the Van der Pol oscillator. By scaling the time variable the equation can be reduced to
![1083_900bc4e9-959d-49b9-bbc8-f432356b9a07.png](https://secure.tutorsglobe.com/CMSImages/1083_900bc4e9-959d-49b9-bbc8-f432356b9a07.png)
Investigate the properties of the Van der Pol oscillator. In particular show that the oscillator shows limit cycle behaviour (that is, the oscillations tend to a form which is independent of the initial conditions and depends only on the parameter μ). Determine the dependence of the limit cycle period on μ.