Hidden-attractor hyperchaotic system generation - ODE problem

Question

Vincent Crasborn 2020-3-18

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/511585-hidden-attractor-hyperchaotic-system-generation-ode-problem

回答： shyam kumarmanickam 2021-3-6

I'm having issues trying to replicate the hyperchaotic field described in the images attached. I'm not mathematician, nor a matlab expert so I might be misunderstanding anything from the notation through to how matlab implemnents this kind of thing.

My problem with the below code is that my values of x,y,z and w rocket off to infinity after a couple iterations, rather than staying between -40 and 40 (roughly) as the plots would suggest.

I wrote my code based on the lorentz field function from the chaotic systems toolbox though I tried to make it as simple as possible. I am trying to replicate the field from this paper.

I would be very thankful for anyone that might have a suggestion as to what I'm doing wrong.

clc; clear; close all;
% Hyperchaotic field 
n = 1000; % number of iterations
% Define all given constants
a = 10;   
b = 25;  
c = -2.5; 
k = 1;  
m = 1;  
% Define the initial conditions:
x0 = 0.2; 
y0 = 0.1;
z0 = 0.75;
w0 = -2;
dot(1,:) = [x0 y0 z0 w0]; % Assigns those intial conditions to ODE solver matrix, and initialise it
% Formulae to implent:
% x' = a*(y-x);      
% y' = -x*z-c*y+k*w; 
% z' = -b+x*y;       
% w' = -m*y;         
for i = 2:n 
    dot(i,1) = a*(dot(i-1,2)-dot(i-1,1));                        %Calculates x'
    dot(i,2) = -dot(i-1,1)*dot(i-1,3)-c*dot(i-1,2)+k*dot(i-1,4); %Calculates y'
    dot(i,3) = -b+dot(i-1,1)*dot(i-1,2);                         %Calculates z'
    dot(i,4) = -m*dot(i-1,2);                                    %Calculates w'
end
% Separate columns of ODE matrix into values for:
x=dot(:,1); % x'
y=dot(:,2); % y'
z=dot(:,3); % z'
w=dot(:,4); % w'
plot3(x,y,z); % Attempt top replicate plot, this command has not worked yet for obvious reasons.