Hi Ozge
I understand that you would like to plot the attractor of the Rössler system.
The Rössler attractor is defined by the following set of ordinary differential equations (ODEs):
dx/dt = -y - z
dy/dt = x + a*y
dz/dt = b + z*(x - c)
Where a, b, and c are system parameters that you can choose. A common choice for these parameters that results in chaotic behavior is a = 0.2, b = 0.2, and c = 5.7.
You can consider following steps to plot the Rössler attractor:
- Define the Rössler equations as a function that MATLAB's ODE solver can use.
- Choose initial conditions and parameters for the system.
- Use an ODE solver like ode45 to numerically integrate the equations.
- Plot the results in a 3D phase space.
Here's an example code for your reference:
% Set the parameters for the Rössler attractor
a = 0.2;
b = 0.2;
c = 5.7;
% Set the initial conditions
x0 = [0; 0; 0]; % Initial condition [x(0), y(0), z(0)]
% Set the time span for the simulation
tspan = [0 100];
% Solve the system using ode45
[t, x] = ode45(@(t,x) rossler(t, x, a, b, c), tspan, x0);
% Plot the attractor
figure;
plot3(x(:,1), x(:,2), x(:,3));
xlabel('x');
ylabel('y');
zlabel('z');
title('Rössler Attractor');
grid on;
% Define the Rössler system as a function
function dx = rossler(t, x, a, b, c)
dx = zeros(3,1); % a column vector
dx(1) = -x(2) - x(3);
dx(2) = x(1) + a*x(2);
dx(3) = b + x(3)*(x(1) - c);
end
Hope this helps!
