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Published on: May 8, 2021
Synchronized states in chaotic systems coupled indirectly through a dynamic environment.
V Resmi1, G Ambika, R E Amritkar
1Indian Institute of Science Education and Research, Pune 411021, India. v.resmi@iiserpune.ac.in
Summary
This study explores chaotic system synchronization via a common environment. Diverse synchronization patterns, including in-phase and antiphase, emerge and are analyzed for stability and transitions.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Coupled chaotic systems can exhibit complex synchronization behaviors.
- Environmental coupling introduces unique dynamics not seen in direct coupling.
- Feedback modulation from systems to the environment adds another layer of complexity.
Purpose of the Study:
- To investigate diverse synchronization phenomena in chaotic systems coupled indirectly through a dynamic environment.
- To analyze the stability and transitions between different synchronization states.
- To compare analytical stability predictions with numerical findings.
Main Methods:
- Utilized approximate stability analysis for synchronization behaviors.
- Performed numerical studies on Rössler and Lorenz systems.
- Analyzed parameter planes of coupling strengths.
- Employed correlation, average phase difference, and Lyapunov exponents for characterization.
Main Results:
- Demonstrated the possibility of various synchronization behaviors: in-phase, antiphase, complete, and antisynchronization.
- Identified transitions to different synchronous states within the parameter plane.
- Found agreement between numerical threshold conditions and stability analysis predictions.
Conclusions:
- Indirect coupling through a dynamic environment enables rich synchronization patterns.
- Stability analysis provides a reliable framework for understanding synchronization transitions.
- The study offers insights into complex system interactions and emergent behaviors.
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