%%% Lotka - Volterra system

	%%% define the right-hand side (vector) function

F = @(X,t) [ 
		X(1) - X(1)*X(2) ;
		-X(2) + X(1)*X(2)
		];



N=80;	%%% number of division points
T=8;	%%% length of time interval

I = linspace(0,T,N);		%%% interval [0,T] with N division points
X0 = [ .2 ; .2 ];			%%% initial condition


X = lsode( F , X0 , I );	%%% SOLVE IT!

axis square;  grid on;
plot( X(:,1) , X(:,2) , '-k' )	%%% plot in the plane

pause	%% wait to see the picture

clf;	%% clear the picture, and
		%% plot with respect to time axis

axis square; hold on; grid on;
plot(I,X(:,1),'-b');
plot(I,X(:,2),'-r');
legend('X_1','X_2');


pause


