% Chapter 8 - Planar Systems.
% Program_8c - Phase Portrait of a Nonlinear System (Fig. 8.12).
% Copyright Birkhauser 2013. Stephen Lynch.

% Phase portrait of a nonlinear system of ODE's.
% IMPORTANT - Program_8a is vectorfield.m.
clear
% sys=inline('[x(2);x(1)*(1-(x(1))^2)+x(2)]','t', 'x');
sys = @(t,x) [x(2);x(1)*(1-(x(1))^2)+x(2)]; 
vectorfield(sys,-3:.5:3,-3:.5:3);
     hold on
     sep=1;
     for x0=-3:sep:3
         for y0=-3:sep:3
            [ts,xs] = ode45(sys,[0 6],[x0 y0]);
            plot(xs(:,1),xs(:,2))
         end
     end
     for x0=-3:sep:3
         for y0=-3:sep:3
            [ts,xs] = ode45(sys,[0 -6],[x0 y0]);
            plot(xs(:,1),xs(:,2))
         end
     end
     hold off
axis([-3 3 -3 3])
fsize=15;
set(gca,'XTick',-3:1:3,'FontSize',fsize)
set(gca,'YTick',-3:1:3,'FontSize',fsize)
xlabel('x(t)','FontSize',fsize)
ylabel('y(t)','FontSize',fsize)
hold off

% End of Program_8c.