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Approximating hidden chaotic attractors via parameter switching
Marius-F Danca1, Nikolay V Kuznetsov2, Guanrong Chen3
1Department of Mathematics and Computer Science, Avram Iancu University of Cluj-Napoca, Cluj-Napoca, Romania.
Chaos (Woodbury, N.Y.)
|February 3, 2018
Summary
This study introduces a parameter switching algorithm to approximate hidden chaotic attractors in nonlinear systems. The method effectively simulates these complex dynamics, offering a new approach for analyzing chaotic behavior.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Computational Physics
Background:
- Hidden chaotic attractors are complex phenomena in nonlinear systems that are difficult to approximate.
- Existing methods may not accurately capture the behavior of these attractors.
Purpose of the Study:
- To investigate and approximate hidden chaotic attractors in a general class of nonlinear systems.
- To introduce and validate the parameter switching (PS) algorithm for this purpose.
Main Methods:
- Utilized the parameter switching (PS) algorithm, involving numerical solutions of initial value problems.
- Switched the control parameter within a predefined set of values.
- Averaged the control parameter with switched values to represent the hidden chaotic attractor.
Main Results:
- The PS-generated attractor closely approximates the attractor obtained by averaging the control parameter.
- Successfully simulated hidden chaotic attractors in the generalized Lorenz and Rabinovich-Fabrikant systems.
- Demonstrated the efficacy of the PS algorithm in approximating complex chaotic dynamics.
Conclusions:
- The parameter switching algorithm provides an effective method for approximating hidden chaotic attractors.
- This approach enhances the understanding and analysis of chaotic systems.
- The study validates the PS algorithm on established chaotic systems.
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