How to train EEG signal on a single chaotic rossler attractor?

clc

clear all

close all

a=0.2;

omega=

b=0.2;

c=5.7;

t(1)=0.0; % Initial t

x(1)=0.001;

y(1)=0.001;

z(1)=0.01; % Initial x,y,z

dt=0.005; % Time step

nn=20000; % Number of time steps

for k=1:nn % Time loop

k

fx=-y(k)-z(k); % RHS of x equation

fy=x(k)+a*y(k); % RHS of y equation

fz=b+z(k).*x(k)-c*z(k); % RHS of z equation

x(k+1)=x(k)+dt*fx; % Find new x

y(k+1)=y(k)+dt*fy; % Find new y

z(k+1)=z(k)+dt*fz; % Find new z

t(k+1)=t(k)+dt; % Find new t

end % Close time loop

figure(1)

plot3(x,y,z)

figure(2)

plot(x,y)

figure(3)

plot(t,x)

figure(4)

plot(t,y)

figure(5)

plot(t,z)

%%

here the code is all about three state variables of rossler attractor(x,y,z). Where a,b,c are the parameter.

How to excite rosller system with external input signal. Then what will be the state equation?

I am beginner of non linear dynamics .help me.

[Sayan Ghosh]

If any one can any document regarding modeling of EEG signal using chaotic oscillator.That also be fine for me

Answer 1

[Sanju]

Hi @Sayan Ghosh,

I understand that you aim to stimulate the Rossler system using an external input.

To excite the Rossler system with an external input signal, you can add the input signal as an additional term in the state equations. The state equations for the Rossler system with an external input signal can be written as:

dx/dt = -y - z + u dy/dt = x + ay dz/dt = b + z(x - c)

where “u” is the external input signal.

To implement this in MATLAB, you can modify the existing code by adding the input signal term to the state equations and updating the loop accordingly.

clc
clear all
close all  

a=0.2;
b=0.2;
c=5.7;
u=0.5; %Amplitude of the signal
f=1; % Frequency of input signal
t(1) = 0.0; % Initial t 
x(1) = 0.001; 
y(1) = 0.001;  
z(1) = 0.01; % Initial x,y,z  
dt = 0.005; % Time step 
nn = 20000; % Number of time steps

for k = 1:nn % Time loop 
     fx = -y(k) - z(k) + u*sin(2*pi*f*t(k)); % RHS of x equation with input signal
     fy = x(k) + a*y(k);
     fz = b + z(k)*(x(k) - c);
     x(k+1) = x(k) + dt*fx;
     y(k+1) = y(k) + dt*fy;
     z(k+1) = z(k) + dt*fz;
     t(k+1) = t(k) + dt;
end % Close time loop

figure(1) 
plot3(x,y,z) 
figure(2) 
plot(x,y) 
figure(3) 
plot(t,x)
figure(4)
plot(t,y)
figure(5) 
plot(t,z)

In this modified code, the input signal is a sine wave with amplitude “u” and frequency “f”. The input signal is added to the x equation, and the sine function is evaluated at the current time step t(k).

The Rossler system can also be excited with other types of input signals, such as a square wave or a sawtooth wave. To do this, you can replace the sine function in the input signal term with the desired waveform.

Hope this Helps!

Thanks.