## Abbildungen - Kapitel 13

 ``` 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 ``` ``` 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 ``` ``` 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); ``` ``` 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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