% This is the main function to solve 
% the LotkaVolterra model in p.224, Mathematical Models in Biology
% example of figure 6.8(a) in p.228

global a b c d

a = 1;
b = 0.5;
c = 0.75;
d = 0.25;

options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4]);

t0 = 0;
tfinal = 10;


N1_ini = [1 2 3 4 5 6];
N2_ini = [2 2 2 2 2 2];

for ind = 1:6

y_ini = [N1_ini(ind) N2_ini(ind)];

[T,y] = ode45(@test1_eqn,[t0 tfinal],y_ini,options);

% plot N2 versus N1

figure(1);hold on; plot(y(:,1),y(:,2));
xlabel('x_1')
ylabel('x_2')
axis equal; box on
end