Code covered by the BSD License

# Dynamical Systems with Applications using MATLAB

### Stephen Lynch (view profile)

13 Sep 2002 (Updated )

Companion Software.

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

Program_8c.m
```% 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.```