The driven van der Pol oscillator is described by the equation of motionwhere α is the amp...

The driven van der Pol oscillator is described by the equation of motion

where α is the amplitude of the driving force and ω is the driving frequency. Let x = x = , y and z = ωt. Solve tire equation numerically in terms of these variables. Let tire oscillator start at (x0, y0, z0) = (0,0,0). Let the emotion evolve for 100 drive cycles (1 drive period = 2π/ω). (1) Make a phase-space plot of its motion. (2) Make a plot of its position versus number of drive cycles. (3) Make a three-dimensional phase-space plot of the first 10 drive cycles. Assume the following conditions.

(a) α =0.1, γ=0.05, ω=1.

(b) α =5, γ = 5, ω = 2.466. Which state is periodic? Chaotic?