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Chaos synchronization basing on symbolic dynamics with nongenerating partition
Xingyuan Wang1, Mogei Wang, Zhenzhen Liu
1School of Electronic and Information Engineering, Dalian University of Technology, Liaoning 116024, People's Republic of China.
Chaos (Woodbury, N.Y.)
|July 2, 2009
Summary
Information theory reveals that chaos synchronization in coupled oscillators requires less channel capacity with nongenerating partitions, despite potential errors. High-quality detectors or lag response can ensure synchronization accuracy.
Area of Science:
- Nonlinear Dynamics
- Information Theory
- Systems Engineering
Background:
- Coupled oscillators are fundamental in many scientific and engineering fields.
- Synchronization of chaotic systems presents unique challenges due to inherent unpredictability.
- Understanding information transmission is crucial for achieving reliable synchronization.
Purpose of the Study:
- To investigate the information transmission requirements for synchronizing unidirectionally coupled chaotic oscillators.
- To compare the efficiency of generating versus nongenerating partitions in chaos synchronization.
- To propose a practical synchronization scheme using symbolic dynamics.
Main Methods:
- Symbolic dynamics for system analysis.
- Information theory to quantify information transmission.
- Analysis of synchronization error and channel capacity.
- Development of a novel synchronization scheme.
Main Results:
- Nongenerating partitions can achieve chaos synchronization with lower channel capacity but may increase synchronization error.
- A critical synchronization error threshold exists for nongenerating partitions.
- Detector quality and response timing (lead/lag) significantly impact synchronization accuracy.
- A practical synchronization scheme based on a nongenerating partition was successfully demonstrated.
Conclusions:
- Information theory provides valuable insights into the trade-offs between channel capacity and synchronization error.
- The choice of partition (generating vs. nongenerating) affects synchronization efficiency.
- Robust synchronization can be achieved through careful detector design and response strategy, even with imperfect partitions.
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