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?

Question

kathiresan 2022-12-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1871607-use-ode-45-in-chua-s-system-with-non-linear-function-need-to-be-solved-but-i-don-t-know-how-iterate

编辑： Torsten 2022-12-13

[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

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Answer 1

Torsten 2022-12-5

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1871607-use-ode-45-in-chua-s-system-with-non-linear-function-need-to-be-solved-but-i-don-t-know-how-iterate#answer_1120622

在 MATLAB Online 中打开

[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

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kathiresan 2022-12-13

在 MATLAB Online 中打开

@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 2022-12-13

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 2022-12-13

编辑：Torsten 2022-12-13

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).

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