Implement logistic ing in MATLAB

 

If the evolution of a system is very sensitive to the initial state, it is called a chaotic system.

The mathematical expression of logistic ing is as follows:

Xn + 1 = μ Xn (n) μ ε [] x ε []

Here, μ, [] is called the logistic parameter. Studies have shown that when xε [], logistic ing is in a chaotic state, that is, the sequence generated by the initial condition x0 under logistic ing is non-cyclical and non-convergent, beyond this range, the generated sequence will surely converge to a specific value.

My program has completed the following functions:

That is to say, when the x0 value is certain, for different μ values, the possible values of iteration are drawn using the parameter μ as the abscissa, and the value after iteration of X as the ordinate

The points in the figure indicate all possible values of X. We can see that the closer the μ value is to 4, the closer the X value range is to the average distribution in the entire 0-1 area, therefore, the Logistic Control Parameter we need to select should be closer to 4, the better.

The logistic equation is that, when a few initial variables are changed, the iterations will be much different. This is the butterfly effect.
For the equation itself, when μ is close to 4, the X value begins to become more disordered and chaos occurs. Therefore, this equation can be understood as the entrance to chaos.

M file:
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Function logistic ()

Clear;
CLF;
U = 2.6: 0.001: 4.0;
X = 0.1;
For I = 1:300
X = U. * (X-X. ^ 2 );
End
For j = 1: 80
X = U. * (X-X. ^ 2 );
Plot (u, X, 'K. ', 'markersize', 2)
Hold on;
End
Grid on

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