my program is not working properly

function kk2

close all; clear all;

% accuracy

%options = odeset('RelTol',1e-9,'AbsTol', 1e-16);

[t,y]=ode45(@f,[0 100],[0.1;0.1;0.1+1;0.1;0.1;0.1] );

plot(t,y(:,2),t,y(:,4),t,y(:,6))

function dy=f(t,y)

%x=y(1);y=y(3);z=y(5)

r=28;

b=8/3;

k=10;

dy=zeros(6,1)

dy= [y(2);k^2*y(1)-k^2*y(3)-k*y(1)*y(5)+k*r*y(5)-k*y(3);y(4);b*y(1)*y(5)-y(1)^2*y(3)-k*y(1)*y(3)+k*y(3)*y(5)-r*k*y(1)+k*r*y(3)+y(1)*y(5)-r*y(1)+y(3);y(6);-y(1)^2*y(5)+r*y(1)^2-y(1)*y(3)-k*y(1)*y(3)+k*y(3)^2-b*y(1)*y(3)+b^2*y(5)]

end

end

so sir we want to plot between t,x,t,y

and we want to plot t vs second element of dy t,fourth element t,vs sixth element

[Jan]

@shiv gaur: You have been asked repeatedly to use a proper code formatting. Please read and consider this: https://www.mathworks.com/matlabcentral/answers/help/rtc#rtc_summary . Thanks.

Answer 1

[Sam Chak]

Hi @shiv gaur

It appears that the system is highly unstable and all states blow up at around 0.35 sec except for . Please check the state equations again. Sometimes, the plus/minus signs can make a huge difference.

Edit: It has some similarities like the Lorenz system, because I recognized the magic values: 10, 8/3, 28.

clear all; clc

r = 28;
b = 8/3;
k = 10;

tspan = linspace(0, 0.3, 10001)';
fun = @(t, y) [y(2); ...
             k^2*y(1) - k^2*y(3) - k*y(1)*y(5) + k*r*y(5) - k*y(3); ...
             y(4); ...
             b*y(1)*y(5) - y(1)^2*y(3) - k*y(1)*y(3) + k*y(3)*y(5) - r*k*y(1) + k*r*y(3) + y(1)*y(5) - r*y(1) + y(3); ...
             y(6); ...
             - y(1)^2*y(5) + r*y(1)^2 - y(1)*y(3) - k*y(1)*y(3) + k*y(3)^2 - b*y(1)*y(3) + b^2*y(5)];
[t, y] = ode45(fun, tspan, [0.1, 0.1, 1.1, 0.1, 0.1, 0.1]);
plot(t, y)

Once you have fixed the model, please ensure that all states can propagate at least until your desired final time, sec, and then you can choose what you want to plot.

[shiv gaur]

how we plot t,second element t vs fourth element t vs six element in equation

[Sam Chak]

Try this:

plot(t, y(:, 2), t, y(:, 4), t, y(:, 6))

[shiv gaur]

Warning: Failure at t=3.541457e-01. Unable to meet integration tolerances without reducing the step size below the

smallest value allowed (8.881784e-16) at time t.

this is the error

[Sam Chak]

Thought I have put my explanations above. The nature of your state equations is highly unstable. It cannot integrate the system pass 0.3541457 sec. That's why I simulated until 0.3 sec to show you the divergence of the states.

If you are very sure that your system is stable, please double check all 6 state equations, especially on the plus/minus signs. Both human error or publishing error (on the reference) can happen.

It's a very common error. So, no worries. You will find it if you look harder.

Would you tell what the system is? Is it a kind of attractor?

[Sam Chak]

Hi @shiv gaur

Have you double checked the mathematical equations of your system? Since you didn't tell us what kind of system it is, and your supplied ODEs have been verified by the ode45 solver, there seems nothing wrong with the program itself. If you are very sure that the system is stable, then my guess is that one or more of the terms in the state equations must be the root cause of the instability.

[Jan]

@Sam Chak: Thanks for your effort. If a user ignores your help consequently, this is his problem.