5d hyperchaotic system implementation

Question

Naman Chugh 2020-3-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/511313-5d-hyperchaotic-system-implementation

回答： Hasnain 2023-3-22

在 MATLAB Online 中打开

Hi,

I am trying to implement 5d hyperchaotic system to generate a hyperchaotic sequence.

The system is described by the following equations:-

˙ x1 = a (x2 − x1) + x4 + x5

˙ x2 = cx1 − x1x3 − x2

˙ x3 = x1x2 − bx3

˙ x4 = −x1x3 + px4

˙ x5 = qx1

The values of parameters - a, b, c, p and q are 10, 8/3, 28, 1.3 and 2.5, respectively.

Initial states of the 5D hyper-chaotic system are x1 (0) = 0.325, x2 (0) = 0.476, x3 (0) = 1.256, x4 (0) = 0.628 and x5 (0) =1.5.

I am trying to generate a hyperchaotic sequence by the following code:-

I = imread('rgb3.jpg');
[m n p] = size(I);
x1(1) = 0.325;   %initial values 
x2(1) = 0.476;
x3(1) = 1.256;
x4(1) = 0.628;
x5(1) = 1.5;
a = 10;         
b = 8/3;
c = 28;
p = 1.3;
q = 2.5;
for i =1:1:m*n
    x1(i+1) = a*(x2(i) - x1(i)) + x4(i) + x5(i)
    x2(i+1) = c*x1(i) - x1(i)*x3(i) - x2(i);
    x3(i+1) = x1(i)*x2(i) - b*x3(i);
    x4(i+1) = - x1(i)*x3(i) + p*x4(i);
    x5(i+1) = q*x1(i);
end     

After 14 iterations the value of x1,x2,x3,x4,x5 turns out to be infinity and subbsequently after that it results in NaN(Not a number). How can i fix this issue so that I can get a hyperchaotic sequence with which I can scramble my image?

Image has to be scrambled separately in the R,G, B planes with the 3 sequences to be chosen from (X1,X2,X3,X4,X5).

Please help me out with this!