Zero lag synchronization of chaotic systems with time delayed couplings

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Optoelectronics and Laser Physics
• Complex Systems Synchronization

Background:

• Zero-lag synchronization (ZLS) is a phenomenon where two chaotic systems synchronize without any time delay between them.
• Previous studies often required specific system configurations or relay units for ZLS, limiting its practical application.
• Understanding the role of coupling delays is crucial for achieving ZLS in complex chaotic systems.

Purpose of the Study:

• To experimentally demonstrate and numerically verify a novel mechanism for achieving zero-lag synchronization (ZLS) in chaotic systems.
• To investigate the influence of multiple mutual coupling delay times on the possibility of ZLS.
• To analyze the stability conditions for ZLS using theoretical tools like the Schur-Cohn theorem.

Main Methods:

• Experimental demonstration using two mutually coupled chaotic semiconductor lasers.
• Numerical simulations of mutually coupled chaotic maps.
• Stability analysis of synchronization using the Schur-Cohn theorem for polynomial roots.

Main Results:

• Zero-lag synchronization (ZLS) was successfully achieved in mutually coupled chaotic semiconductor lasers.
• The study found that ZLS requires two mutual coupling delay times with specific integer ratios, not achievable with a single delay time.
• Numerical analysis confirmed this mechanism for chaotic maps, with stability dictated by polynomial root locations and specific integer ratios.

Conclusions:

• A new mechanism enabling zero-lag synchronization (ZLS) in chaotic systems is presented, relying on multiple coupling delays.
• The findings highlight the critical role of specific integer ratios between delay times for achieving ZLS.
• This research provides a generalized understanding of ZLS in systems with multiple delay couplings.