vanderpol-modulated.mws

>    restart;

>    ode := diff(u(t),t,t)+u(t)=-eps*diff(u(t),t)*(u(t)^2-sin(t*eps^2));

ode := diff(u(t),`$`(t,2))+u(t) = -eps*diff(u(t),t)*(u(t)^2-sin(t*eps^2))

>    eps := 0.2;

eps := .2

>    sol := dsolve({ode, u(0)=1, D(u)(0)=0}, numeric, maxfun=0);

sol := proc (x_rkf45) local res, data, vars, solnproc, outpoint, ndsol, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 14; if _...

>   

>    with(plots):

>    odeplot(sol, [t, u(t)], 0..2000, numpoints=10000);

[Maple Plot]

>    pic := %:

>    ode2 := diff(A(tau),tau)=-A(tau)^3/8+sin(tau*eps)*A(tau)/2;

ode2 := diff(A(tau),tau) = -1/8*A(tau)^3+1/2*sin(.2*tau)*A(tau)

>    sol2 := dsolve({ode2, A(0)=1}, numeric);

sol2 := proc (x_rkf45) local res, data, vars, solnproc, outpoint, ndsol, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 14; if ...

>    odeplot(sol2, [tau/eps, A(tau)], tau=0..2000*eps, numpoints=400, color=black, thickness=3);

[Maple Plot]

>    pic2 := %:

>    display(pic2, pic);

[Maple Plot]

>   

>   

>