Question

Explain for the Van Der Pol oscillator, why the limit cycle depends on the parameter μ. (Answer should be in terms of |y| and μ)

Answer 1

First order system of differential equations dx dx dt Numerical integration on last equations shows that every initial condition (x-0,x 0) Approaches a unique periodic motion. Nature of this limit cycle is dependent on the value μ. for small values of μ the motion is nearly sinusoidal, whearas for large values μ it is a relaxation oscillation. Meaning that it tends to resemble a series of step functions, jumping between positive and negative values twice per cycle