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sketch a phase portrait for the nonlinear system

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106510] sketch a phase portrait for the nonlinear system
  • From: æ æ <hongtao826 at yahoo.com.cn>
  • Date: Fri, 15 Jan 2010 03:17:11 -0500 (EST)

Hi,everyone,
I am new in Mathematica.When I try to sketch a phase portrait for the nonlinear system, I don't know how to plan the input values for the ODEs to get the right FIGURE.
My example is from a book as follows:
ode1[x0_,y0_]:=NDSolve[{x=E2=80=99[t]==y[t],y=E2=80=99[t]==x[t](1-(x[t])^2)+y[t],x[0]==x0,y[0]==y0},{x[t],y[t]},{t,-10,10}];
sol[1]=ode1[0.1,0.16];sol[2]=ode1[0.1,-0.06];
sol[3]=ode1[-0.1,-0.16];sol[4]=ode1[-0.1,0.06];
sol[5]=ode1[1.3,0];sol[6]=ode1[-1.3,0];
p=ParametricPlot[Evaluate[Table[{x[t],y[t]}/.sol[i],{i,6}]],{t,-10,10},PlotRange->{{-3,3},{-3,3}}];
Show[p,PlotRange->{{-3,3},{-3,3}},AxesLabel->{"x","y"}]
Would you like to tell me why we choose the input values for the ODEs such as ode1[0.1,0.16]; ode1[0.1,-0.06];...? You see, when I tried to change the values ,I can't see the figure any more.
Best Regards,
hongtao


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