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Zero-lag synchronization and multiple time delays in two coupled chaotic systems.

Meital Zigzag¹, Maria Butkovski, Anja Englert

¹Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

Summary

This study demonstrates how to achieve zero-lag synchronization (ZLS) in complex chaotic systems with multiple feedbacks and couplings. The findings suggest ZLS is possible across a broad range of coupling delays, benefiting communication networks.

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Area of Science:

Nonlinear Dynamics
Chaos Theory
Synchronization Phenomena

Background:

Zero-lag synchronization (ZLS) is crucial for coupled chaotic systems but traditionally limited by specific delay ratios.
Extending ZLS to systems with multiple self-feedbacks and mutual couplings presents a significant challenge.

Purpose of the Study:

To generalize the conditions for achieving ZLS in chaotic systems with multiple feedback and coupling delays.
To explore the analytical and numerical feasibility of ZLS under these extended conditions.

Main Methods:

Analytical derivation of ZLS conditions for multiple delays.
Numerical simulations using Bernoulli maps and Lang-Kobayashi equations.
Investigation of the impact of varying mutual coupling delays.

Main Results:

ZLS is achievable when the sum of weighted self-feedback delays and mutual coupling delays equals zero (SigmaliNdi+igmamjNcj=0).
The study confirms ZLS can be achieved for a continuous range of mutual coupling delays.
Results were validated using both theoretical models and numerical simulations.

Conclusions:

The generalized conditions for ZLS are robust and applicable to complex chaotic systems.
The ability to achieve ZLS over a continuous range of delays has significant implications for secure communication networks.
This research expands the understanding and application of synchronization in chaotic systems.