I have the following system $$ \ddot{x} + 0.6\dot{x} + 3x + x^{2} = 0 $$
In the book I'm reading, the phase portrait of the nonlinear system for the aforementioned equation is

I would like to get same result in Matlab. This is what I did
function output = F(t, x)
output = [ x(2);
-0.6*x(2) - 3*x(1) - x(1)^2];
end
and this is the main function
clear all
clc
x0 = 1;
xdot0 = 1;
t = 0:0.01:10;
X0 = [x0, xdot0];
[T X] = ode45(@F, t, X0);
figure(1)
clf
plot(X(:,1), X(:,2))
title('The Phase Portrait of a nonlinear system');
xlabel('x');
ylabel('xdot');
I'm not getting same result. My question is how can I modify the code to get same result?
Edit: Now it is working with the following code.
function output = F(t, x)
output = [ x(2);
-0.6*x(2) - 3.*x(1) - x(1)^2];
end
The main.m
t = 0:0.1:8;
X0 = [-3, 4.5];
[T X] = ode45(@F, t, X0);
figure(1)
clf
plot(X(:,1), X(:,2))
title('The Phase Portrait of a nonlinear system');
xlabel('x');
ylabel('xdot');
axis([-9 9 -10 10])
grid on
hold on
X0 = [4, 8];
[T X] = ode45(@F, t, X0);
plot(X(:,1), X(:,2))
hold on
X0 = [-1, 2];
[T X] = ode45(@F, t, X0);
plot(X(:,1), X(:,2))
hold on
X0 = [-7, 6];
[T X] = ode45(@F, t, X0);
plot(X(:,1), X(:,2))
hold on
X0 = [-8, 5];
[T X] = ode45(@F, t, X0);
plot(X(:,1), X(:,2))
hold on
X0 = [-5.5, 9];
[T X] = ode45(@F, t, X0);
plot(X(:,1), X(:,2))
hold on
X0 = [-2.5, 8];
[T X] = ode45(@F, t, X0);
plot(X(:,1), X(:,2))