Interpretation:
To write the program to compute the
Concept Introduction:
An attractor that come out in a simplified system of equations which describes two-dimensional fluid flow of uniform depth is known as Lorenz attractor.
It is a system of ordinary differential equation.
Answer to Problem 1E
Solution:
The Matlab program is written to compute the correlation dimension of the Lorenz attractor.
The slope of the second figure depends on the value of correlation; hence, the dimension depends on r.
Explanation of Solution
Using Matlab, we can write a program to compute the correlation dimension of the Lorenz attractor.
By running the above Matlab code, we get the Lorenz attractor correlation as below:
This is the correlation dimension of Lorenz attractor.
Now consider the slope to be
Now use the below Matlab code to reproduce the figure
Hence, this is the required curve.
The slope of the above figure depends on the value of correlation; hence, the dimension depends on r.
The correlation dimension of the Lorenz attractor is computed. The slope of the figure depends on the value of correlation; hence, dimension depends on r.
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Chapter 11 Solutions
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
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