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eps = 0.1;
[x,y] = meshgrid(-3:0.6:3,-3:0.6:3);
u = y; v = eps*(1-x.^2).*y-x;
h = quiver(x,y,u,v,1.9); hold on;
set(h,'linewidth',2.5,'color',[0.7 0.7 0.7]);
h = plot(0,0,'k.'); set(h,'markersize',40);
opt=odeset('RelTol',1e-5);
[t,xt]=ode45(@vdpo,[0 30],[1.5;1.5],opt);
h=plot(xt(:,1),xt(:,2),'k'); set(h,'linewidth',2);
[t,xt]=ode45(@vdpo,[0 30],[3;2],opt);
h=plot(xt(:,1),xt(:,2),'k'); set(h,'linewidth',2);
axis(3*[-1 1 -1 1]); axis square
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eps = 2;
[x,y] = meshgrid(-3:0.6:3,-4:0.8:4);
u = y; v = eps*(1-x.^2).*y-x;
h = quiver(x,y,u,v,4); hold on;
set(h,'linewidth',2.5,'color',[0.7 0.7 0.7]);
h = plot(0,0,'k.'); set(h,'markersize',40);
opt=odeset('RelTol',1e-5);
[t,xt]=ode45(@vdpo,[0 20],[0.1;0.1],opt);
h=plot(xt(:,1),xt(:,2),'k'); set(h,'linewidth',2);
axis([-2.3 2.3 -4 4]); axis square
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a = 1; c = 0.75; d = 0.8; e = 1;
[x,y] = meshgrid(0:0.25:3,0:0.25:4);
u = (a-c*y).*x; v = (-d+e*x).*y;
h = quiver(x,y,u,v,1.9); hold on;
set(h,'linewidth',2.5,'color',[0.7 0.7 0.7]);
h = plot(0,0,'k.'); set(h,'markersize',40);
h = plot(d/e,a/c,'k.'); set(h,'markersize',40);
dgl = inline('[(1-0.75*x(2)).*x(1);(-0.8+1*x(1)).*x(2)]','t','x');
opt=odeset('RelTol',1e-5);
[t,xt]=ode45(dgl,[0 30],[1.5;1.5],opt);
h=plot(xt(:,1),xt(:,2),'k'); set(h,'linewidth',2);
[t,xt]=ode45(dgl,[0 30],[2;2],opt);
h=plot(xt(:,1),xt(:,2),'k'); set(h,'linewidth',2);
[t,xt]=ode45(dgl,[0 30],[0.5;0.5],opt);
h=plot(xt(:,1),xt(:,2),'k'); set(h,'linewidth',2);
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h = plot(t,xt(:,1),'k-.'); set(h,'linewidth',2); hold on
h = plot(t,xt(:,2),'k-*'); set(h,'linewidth',2);
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