How do I plot the attractor of Rössler?

I want to plot attractor of Rössler for a signal. How can I do?

Answer 1

[Vaibhav]

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:

1. Define the Rössler equations as a function that MATLAB's ODE solver can use.
2. Choose initial conditions and parameters for the system.
3. Use an ODE solver like ode45 to numerically integrate the equations.
4. 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!