Information theoretic approach to quantify complete and phase synchronization of chaos

Area of Science:

• Nonlinear Dynamics
• Information Theory
• Chaos Theory

Background:

• Chaotic synchronization is a phenomenon observed in nonlinear systems where distinct chaotic oscillators exhibit correlated dynamics.
• Quantifying the degree of synchronization is crucial for understanding complex systems in physics, biology, and engineering.
• Existing methods may be sensitive to noise and signal imperfections.

Purpose of the Study:

• To propose a novel quantitative characteristic for evaluating the degree of chaotic synchronization.
• To validate the proposed characteristic using information theory principles.
• To assess the robustness of the characteristic against noise and signal distortion.

Main Methods:

• Development of a quantitative characteristic based on information theory.
• Application and testing of the characteristic for complete synchronization of chaos.
• Application and testing of the characteristic for phase synchronization of chaos.

Main Results:

• A new information theory-based quantitative characteristic for chaotic synchronization is proposed.
• The characteristic effectively evaluates both complete and phase synchronization.
• The proposed characteristic demonstrates stability and reliability in the presence of small noise and nonlinear signal distortion.

Conclusions:

• The developed quantitative characteristic provides a robust measure for chaotic synchronization.
• This approach offers a reliable tool for analyzing complex nonlinear systems.
• The stability against noise and distortion enhances its applicability in real-world scenarios.