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');



→ Zurück zur Homepage www.dgl-buch.de

© 2008 Lars Grüne, Oliver Junge