r=2; K=1.4; s=1; c=0.5; a=2; d=0.1;
x=-1.2:0.01:2.5; y=0:0.02:4;
[X,Y]=meshgrid(x,y);
U=r*(1-X/K)-s*Y./(a*X+1);
V=c*s*X./(a*X+1)-d;
cvals=[0 0];
hold on
contour(x,y,U,cvals,'k--');
contour(x,y,V,cvals,'k--');
[T1,Y1] = ode45('predprey',[0 160],[1.5 3.5]);
[T2,Y2] = ode45('predprey',[0 160],[1.5 2.5]);
[T3,Y3] = ode45('predprey',[0 160],[1.5 1.5]);
[T4,Y4] = ode45('predprey',[0 160],[0.1 0.1]);
[T5,Y5] = ode45('predprey',[0 200],[0.3 2.2]);
[T6,Y6] = ode45('predprey',[0 160],[1.5 0.1]);
for i=1:4
    [Si,Xi] = ode45('predprey',[0 160],[0.08*i .5*i]);
    plot(Xi(:,1),Xi(:,2),'g','LineWidth',1);
end
option=odeset('AbsTol',1e-9,'RelTol',1e-9);
plot(Y1(:,1),Y1(:,2),'r','LineWidth',1);
plot(Y2(:,1),Y2(:,2),'r','LineWidth',1);
plot(Y3(:,1),Y3(:,2),'r','LineWidth',1);
plot(Y4(:,1),Y4(:,2),'b','LineWidth',1);
plot(Y5(:,1),Y5(:,2),'k','LineWidth',1);
plot(Y6(:,1),Y6(:,2),'g','LineWidth',1);
xlim([0 1.5]);
text(0.8,3.8,'dx/dt=rx(1-x/K)-sxy/(ax+1)','FontSize',12);
text(0.8,3.5,'dy/dt=y(csx/(ax+1)-d)','FontSize',12);
title('Predator-prey interaction, r=2 K=1.4 s=1 c=0.5 a=2 d=0.1','FontSize',12)
xlabel('prey'),
ylabel('predator');
ylim([0 4]);