Symbolic dynamics-based error analysis on chaos synchronization via noisy channels
Da Lin1, Fuchen Zhang2, Jia-Ming Liu3
1School of Automatic and Electronic Information, Sichuan University of Science and Engineering, Zigong 643000, China and Electrical Engineering Department, University of California, Los Angeles, Los Angeles, California 90095, USA.
Summary
Symbolic dynamics simplifies chaotic systems for error analysis in noisy channels. Optimizing word length and partition regions minimizes chaos synchronization errors, as shown by numerical simulations.
Area of Science:
- Nonlinear Dynamics and Chaos Theory
- Information Theory and Signal Processing
Background:
- Chaos synchronization is crucial for secure communication.
- Transmitting chaotic signals through noisy channels introduces synchronization errors.
- Symbolic dynamics offers a method to analyze and potentially mitigate these errors.
Purpose of the Study:
- To investigate chaos synchronization errors in noisy channels using symbolic dynamics.
- To develop a coder-decoder scheme based on symbolic dynamics for error reduction.
- To model the relationship between symbolic dynamics parameters and synchronization error.
Main Methods:
- Applying symbolic dynamics to transform chaotic systems into discrete symbol sequences (shift maps).
- Developing a coder-decoder scheme leveraging the symbolic representation.
- Formulating a mathematical model relating word length, partition region number, and synchronization error.
Main Results:
- A model quantifying the trade-off between word length and region number for minimizing synchronization error was established.
- The proposed coder-decoder scheme effectively utilizes symbolic dynamics for error analysis.
- Numerical simulations validated the theoretical model and the effectiveness of the approach.
Conclusions:
- Symbolic dynamics provides a powerful framework for analyzing and managing chaos synchronization errors.
- Optimization of symbolic representation parameters (word length, region number) is key to minimizing synchronization errors.
- The study demonstrates a practical method for improving the reliability of chaos synchronization in noisy environments.
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