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Dominant Attractor in Coupled Non-Identical Chaotic Systems
Dorsa Nezhad Hajian1, Sriram Parthasarathy2, Fatemeh Parastesh1
1Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran.
Entropy (Basel, Switzerland)
|December 23, 2022
Summary
Coupling non-identical chaotic oscillators can alter their dynamics. This study found that the dominant attractor, less affected by coupling, typically possesses a larger largest Lyapunov exponent, indicating greater inherent chaos.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Coupled non-identical chaotic oscillators exhibit complex dynamical behaviors.
- Incoherent dynamics can lead to structural degradation of phase space attractors.
Purpose of the Study:
- Investigate attractor dominance in coupled Lorenz-Rössler, Lorenz-HR, and Rössler-HR systems.
- Identify factors influencing attractor dominance, such as frequency and amplitude differences.
- Compare the inherent chaotic characteristics of the systems.
Main Methods:
- Coupling analysis of Lorenz-Rössler, Lorenz-HR, and Rössler-HR systems.
- Utilizing a cost function based on return maps for similarity detection.
- Calculating the largest Lyapunov exponent to quantify chaotic behavior.
Main Results:
- The dominant attractor, defined as the least altered by coupling, was identified for each system pair.
- Frequency and amplitude differences were examined for their effects on coupling outcomes.
- A correlation was observed between a larger largest Lyapunov exponent and attractor dominance.
Conclusions:
- The system with the greater largest Lyapunov exponent is generally the dominant attractor in coupled non-identical chaotic oscillator systems.
- Understanding attractor dominance is crucial for predicting the behavior of complex coupled systems.
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