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English: Phase portrait of Van der Pol oscillator. Created in python using scipy, numpy and matplotlib libraries.
from numpy import * from scipy import * from scipy.integrate import odeint from matplotlib.pyplot import * from mpl_toolkits.axes_grid.axislines import SubplotZero def myFun(u,t=0.,mu=.5): x = u v = u dx = v dv = mu*(1.-x**2)*v-x return (dx,dv) t = linspace(-5.5,5.5,300) u0 = array([1.,1.]) mu = [.1, .2, .5, 1., 1.5, 2.0] fig = figure(figsize=(5.5,7)) ax = SubplotZero(fig,111) fig.add_subplot(ax) ax.grid(True) for direction in ["right","top"]: ax.axis[direction].set_visible(False) for m in mu: u = odeint(myFun,u0,t,args=(m,)) ax.plot(u[:,0],u[:,1],lw=1.5,label=r'$\mu=%.1f$'%m) x = linspace(-3,3,15) y = linspace(-4,4,15) x,y = meshgrid(x,y) X,Y = myFun([x,y]) M = (hypot(X,Y)) M[M==0]=1. X,Y = X/M, Y/M ax.quiver(x,y,X,Y,M,pivot='mid',cmap=cm.jet) ax.minorticks_on() ax.legend(handletextpad=0,loc='upper left') setp(ax.get_legend().get_texts(),fontsize=12) fig.savefig("Van_der_pols_equation_phase_portrait.svg",bbox_inches="tight",\ pad_inches=.15)
|Date||15 June 2011|
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