IN PYTHON

C $3\mathrm{.}4$ The driven van der Pol oscillator is described by the equation of motion

$x^{}-(1-x^2)x^{}+x=cost$

where $$ is the amplitude of the driving force and $$ is the driving frequency. Let $x=$

$x,y=x^{},$ and $z=t.$ Solve the equation numerically in terms of these variables.

Let the oscillator start at $(x_0,y_0,z_0)=(0,0,0).$ Let the motion evolve for $100$ drive

cycles $(1$ drive period $=2\frac{}{}.(1)$ 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 ten drive cycles. Assume the following conditions.

$($a$)=0\mathrm{.}1,=0\mathrm{.}05,=1.$

$($b$)=5,=5,=2\mathrm{.}466.$ Which state is periodic? Chaotic?