Zero delay synchronization of chaos in coupled map lattices

Area of Science:

• Nonlinear dynamics
• Complex systems
• Chaos theory

Background:

• Coupled map lattices (CMLs) are widely used models for studying complex spatio-temporal dynamics.
• Synchronization phenomena in coupled dynamical systems are of significant interest in various scientific fields.
• Mutual coupling and time delays are common features in real-world complex systems.

Purpose of the Study:

• To investigate the possibility of zero delay synchronization in mutually coupled map lattices with delay.
• To analytically determine the conditions and parameter regimes for achieving synchronization.
• To assess the robustness of synchronization against parameter mismatches and estimate error bounds.

Main Methods:

• Analytical investigation of synchronization conditions in a system of three mutually coupled map lattices with delay.
• Derivation of parametric regimes leading to zero delay (isochronal) synchronization.
• Estimation of synchronization error bounds to quantify robustness against internal parameter mismatches.

Main Results:

• Demonstration that a third driving coupled map lattice can induce zero delay synchronization in two mutually coupled lattices with delay.
• Analytical estimation of the parameter regions supporting synchronization.
• Evidence that mutual delays can enhance the synchronization process.
• Quantification of the robustness of isochronal synchronization against internal parameter variations.

Conclusions:

• Zero delay synchronization is achievable in mutually coupled map lattices with delay when driven appropriately.
• The presence of mutual delays plays a beneficial role in enhancing synchronization.
• The observed synchronization is robust to internal parameter mismatches, with analytically estimated error bounds providing a measure of this resilience.