mytitle = 'Predator-Prey'; 
xlab = '$t$ (Years after 1900)'; 	
ylab = 'Pelts ($\times 1000$)'; 

load('lynxhare');
p = [34.9134 3.8566 0.48069 0.024822 0.92718 0.027564];

[t,Y] = ode23(@lotvol,[0:0.1:20],[p(1);p(2)],[],p(3),p(4),p(5),p(6));	

plot(t,Y(:,1),'r-','LineWidth',1.5);  
hold on                           
plot(t,Y(:,2),'b-','LineWidth',1.5);
plot(td,hare,'ro','Markersize',7);
plot(td,lynx,'bo','Markersize',7);

grid      
legend('Hare Model','Lynx Model','Hare Data','Lynx Data','Location','Northeast'); 
xlim([0 20]);
ylim([0 80]);

fontlabs = 'Times New Roman'; 
xlabel(xlab,'FontSize',14,'FontName',fontlabs,'interpreter','latex');  
ylabel(ylab,'FontSize',14,'FontName',fontlabs,'interpreter','latex');  
title(mytitle,'FontSize',16,'FontName','Times New Roman','interpreter','latex'); 
set(gca,'FontSize',12);         

print -depsc lynxhare_ts.eps	

figure(2);

mytitle = 'Predator Prey - Phase Portrait';
xlab = 'Hare Pelts ($\times 1000$)'; 
ylab = 'Lynx Pelts ($\times 1000$)';

plot(Y(:,1),Y(:,2),'m-','LineWidth',1.5);  
hold on                           
plot(hare,lynx,'mo','Markersize',7);
plot(33.637,19.365,'o','color',[0,0.6,0],'Markersize',7,'MarkerFaceColor',[0,0.6,0]);

grid      
legend('Model','Data','Equilibrium','Location','Northeast'); 
xlim([0 80]);
ylim([0 70]);

fontlabs = 'Times New Roman'; 
xlabel(xlab,'FontSize',14,'FontName',fontlabs,'interpreter','latex');  
ylabel(ylab,'FontSize',14,'FontName',fontlabs,'interpreter','latex');  
title(mytitle,'FontSize',16,'FontName','Times New Roman','interpreter','latex'); 
set(gca,'FontSize',12);         

print -depsc lynxhare_pp.eps	


