clear all global A % % Example 1 % %A=[[-1 -2];[4 -5]]; A=[[-1 -2];[0 1]]*[[-.50 -1];[1 -.50]]/[[-1 -2];[0 1]]; x1=-1;x2=1;y1=-1;y2=1; [x,y]=meshgrid(x1:.1:x2,y1:.1:y2); t=0; xprime=A(1,1).*x+A(1,2).*y; yprime=A(2,1).*x+A(2,2).*y; nxprime=xprime./sqrt(xprime.^2+yprime.^2); nyprime=yprime./sqrt(xprime.^2+yprime.^2); quiver(x,y,nxprime,nyprime,.5); T=4; xinit=[[-2;1] [2;-1] [1;-1] [-1;1] [1;-.6] [-1;.6] [0;-1] [.5;-1] [0;1] [.5;1]]; K=length(xinit(1,:)); for k=1:K [t,x]=ode23('f',[0, T],xinit(:,k)); hold on plot(x(:,1),x(:,2),'r-','linewidth',2) end axis([-1 1 -1 1]) [t,x]=ode23('f',[0, -T],xinit(:,4)); hold on plot(x(:,1),x(:,2),'r-','linewidth',2)