function hopf

%parameters
a=0.5;
b=0.20;
%intervals of time which to run the model
tspan=[0 100];
%the initial condition for susceptible and infected
x0=[0.95; 0.05];

[t,x]=ode45(@f,tspan,x0);

plot(t,x(:,1),t,x(:,2),'linewidth',2);
xlabel('time');
ylabel('population');
legend('prey', 'predator'), pause

plot(x(:,1),x(:,2),'linewidth',2);
xlabel('prey');
ylabel('predator');

function dxdt=f(t,x)
dxdt=[x(1)*x(1)*x(2)-x(1)+b; -x(1)*x(1)*x(2)+a];
end
end