Use Ode 45 in Chua's system with non linear function need to be solved but I don't know how iterate the non linear function in loop?

[t,x] = ode45(@chua_function,[0 150],[0.1 0.1 0]);
plot3(x(:,1),x(:,2),x(:,3),'r')
title(" Chua's circuit")

xlabel('x')
ylabel('y')
zlabel('zr')
grid

function out = chua_function(~,p)
a = 9; 
B = 14.28; 
m0 = 0.128;
m1= -0.42; 
m2= 2;
m3= - 0.38;
m4= 0.57; 
m5= -0.342;
e1 = 1; 
e2 = 2.15;
e3 = 3.6; 
e4 = 6.2; 
e5 = 9;
x = p(1);
y = p(2);
z = p(3);
g = (m5)*x+0.5*((m0 - m1)*(abs(x+e1)-abs(x-e1))) +(0.5)*((m1- m2)*(abs(x+e2)-abs(x-e2)))
+(0.5)*((m2 - m3)*(abs(x+e3)-abs(x-e3)))+(0.5)*((m3 - m4)*(abs(x+e4)-abs(x-e4)))
+(0.5)*((m4 - m5)*(abs(x+e5)-abs(x-e5)));

%g = (m5)*x+0.5*((m0 - m1)*(abs(x+e1)-abs(x-e1)))
xdot = a*(y-g);
ydot = x - y+ z;
zdot = -B*y;
out = [xdot ydot zdot]';
end

Answer 1

[Torsten]

[t,x] = ode45(@chua_function,[0 150],[0.1 0.1 0]);
plot3(x(:,1),x(:,2),x(:,3),'r')
title(" Chua's circuit")
xlabel('x')
ylabel('y')
zlabel('zr')
grid

function xdot = chua_function(~,x)
  eta = 9; 
  zeta = -14.28; 
  m = [0.9,-3,3.5,-2.7,4,-2.4]/7;
  E = [1,2.15,3.6,6.2,9];
  phix1 = m(end)*x(1) + 0.5*sum((m(1:end-1)-m(2:end)).*(abs(x(1)+E(1:end))-abs(x(1)-E(1:end))));
  xdot = zeros(3,1);
  xdot(1) = eta*(x(2)-phix1);
  xdot(2) = x(1) - x(2) + x(3);
  xdot(3) = zeta*x(2);
end

[kathiresan]

thanks lot .

its quite better but the graph should shows 5 scroll chaotic attractor but here it was 4 scroll attractor only bbut i tried to figured out.

thank for your wonderful code..

[Torsten]

Maybe the time span over which you integrate is too short.

Try

[0 500]

instead of

[0 150]

e.g.

[kathiresan]

yes got it thanks a lot

[kathiresan]

@Torsten

[t,x] = ode45(@chua_function,[0 200],[0.1 0.1 0]);
plot3(x(:,1),x(:,2),x(:,3),'r')
title(" Chua's circuit x")
xlabel('x1')
ylabel('y1')
zlabel('z1')
grid
[t,y] = ode45(@chu_function1,[0 200],[5.13 1.10 -5.50]);
plot3(y(:,1),y(:,2),y(:,3),'r')
title(" Chua's circuit y")
xlabel('x2')
ylabel('y2')
zlabel('z2')
grid
function xdot = chua_function(~,x)
  eta = 9; 
  zeta = -14.28; 
  m = [0.9/7,-3/7,3.5/7,-2.7/7,4/7,-2.4/7];
  E = [1,2.15,3.6,6.2,9];
  phix1 = m(end)*x(1) + 0.5*sum((m(1:end-1)-m(2:end)).*(abs(x(1)+E(1:end))-abs(x(1)-E(1:end))));
  xdot = zeros(3,1);
  xdot(1) = eta*(x(2)-phix1);
  xdot(2) = x(1) - x(2) + x(3);
  xdot(3) = zeta*x(2);
end

function ydot = chu_function1(~,y)
  eta = 9; 
  zeta = -14.28; 
  m = [0.9/7,-3/7,3.5/7,-2.7/7,4/7,-2.4/7];
  E = [1,2.15,3.6,6.2,9];
  phiy1 = m(end)*y(1) + 0.5*sum((m(1:end-1)-m(2:end)).*(abs(y(1)+E(1:end))-abs(y(1)-E(1:end))));
  ydot = zeros(3,1);
  ydot(1) = eta*(y(2)-phiy1);
  ydot(2) = y(1) - y(2) + y(3);
  ydot(3) = zeta*y(2);
end

i have tried same for my response system for same time step with conrol but its not give the same solution vector , do i need to switch to eulers method its goof or ode45 is enough to solve drive and respone system in same time step ???

could you clarify or modify this code to euler method??

[kathiresan]

I have tried same for my response system for same time step with conrol but its not give the same solution vector , do i need to switch to eulers method its goof or ode45 is enough to solve drive and respone system in same time step ???

could you clarify or modify this code to euler method??

[Torsten]

Call ode45 in a loop from t0 to t1, t1 to t2,... and set the initial conditions for y1,y2 and y3 for the new time step from t_k to t_(k+1) as the results from the previous time step + gamma*e_i(t_k) (i=1,2,3).