## Abbildungen - Kapitel 10

 ``` mu = 1; [x,y] = meshgrid(-2:0.5:2,-2:0.5:2); u = x.^2 - mu; v = -y ; h = quiver(x,y,u,v,1.5,'k'); hold on; h = plot(-sqrt(mu),0,'k.'); set(h,'markersize',40); h = plot(sqrt(mu),0,'k.'); set(h,'markersize',40); axis([-2 2 -2 2]); axis square ``` ``` lambda = linspace(0,5,100); x = sqrt(lambda); h=plot([-3 0],[0 0],'k',[0 5],[0 0],'k--',lambda,x,'k',lambda,-x,'k'); axis([-3,5,-2.5,2.5]); ``` ``` x = linspace(-2,2,200); hold on; for y0=linspace(-2,2,9) plot(x,y0.*exp(-1./x(1)).*exp(1./x),'k'); end y0=2; for x0=[-2 -1.5 -1 -0.5 0.5 1.5] plot(x,y0.*exp(-1./x0).*exp(1./x),'k'); end y0=-2; for x0=[-2 -1.5 -1 -0.5 0.5 1.5] plot(x,y0.*exp(-1./x0).*exp(1./x),'k'); end axis([-2 2 -2 2]); axis square ``` ``` mu = 0.5; [x,y] = meshgrid(-1:0.2:1,-1:0.2:1); u = -y-x.*(mu+x.^2+y.^2); v = x-y.*(mu+x.^2+y.^2); h = quiver(x,y,u,v,1.9,'k'); hold on; h = plot(0,0,'k.'); set(h,'markersize',40); axis(0.8*[-1 1 -1 1]); axis square ``` ``` mu = -0.5; [x,y] = meshgrid(-1:0.2:1,-1:0.2:1); u = -y-x.*(mu+x.^2+y.^2); v = x-y.*(mu+x.^2+y.^2); h = quiver(x,y,u,v,1.9,'k'); hold on; h = plot(0,0,'k.'); set(h,'markersize',40); axis(0.8*[-1 1 -1 1]); axis square ``` ``` mu = -1; h=plot([0,1],0,'k.'); hold on; set(h,'markersize',40,'markeredgecolor','k'); pdl = inline('[x(2);x(1)-x(1).^2-0.2*x(2)]','t','x'); opt=odeset('RelTol',1e-5); axis([-1 2 -1.5 1.5]) [t,x]=ode45(pdl,[0 -10],[0.01;0],opt); h=plot(x(:,1),x(:,2),'k'); set(h,'linewidth',2); [t,x]=ode45(pdl,[0 -5],[-0.01;0],opt); h=plot(x(:,1),x(:,2),'k'); set(h,'linewidth',2); [t,x]=ode45(pdl,[0 30],[0.01;0],opt); h=plot(x(:,1),x(:,2),'k'); set(h,'linewidth',2); [t,x]=ode45(pdl,[0 7],[-0.01;0],opt); h=plot(x(:,1),x(:,2),'k'); set(h,'linewidth',2); ``` analog mit `pdl = inline('[x(2);x(1)-x(1).^2]','t','x');` und zusätzlich``` for x1=[-1.5 -1.25 -1 -0.75 -0.5 -0.3 -0.15], [t,x]=ode45(pdl,[0 6],[1;x1],opt); h=plot(x(:,1),x(:,2),'k-'); set(h,'linewidth',2,'color',[0.8 0.8 0.8]); [t,x]=ode45(pdl,[0 -6],[1;x1],opt); h=plot(x(:,1),x(:,2),'k-'); set(h,'linewidth',2,'color',[0.8 0.8 0.8]); end ``` analog mit `pdl = inline('[x(2);x(1)-x(1).^2+0.2*x(2)]','t','x');`

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