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Abstract:
Enhancing synchronization is essential for ensuring smoother operations, optimal resource use, fewer errors, and improved performance in many complex networks. This study presents a novel heuristic strategy using optimized time-varying multi-variable couplings to improve synchronization stability in networks of chaotic systems. The optimization algorithm seeks to find the optimal multi-variable coupling with lower local (finite-time) Lyapunov exponents of the variational equations over short time intervals. Applying this algorithm to paradigmatic oscillators demonstrates a consistent empirical enhancement in synchronization stability. The average local largest Lyapunov exponent, computed over different short time intervals, exhibits significantly more negative values across various normalized coupling strengths than other configurations, including time-varying single-variable and optimized static multi-variable couplings. Moreover, couplings corresponding to diagonal entries of the coupling matrix outperform those related to non-diagonal entries in achieving optimal synchronization. These findings highlight the potential of optimized time-varying multi-variable couplings for enhancing the synchronization stability of networks in diverse applications, such as neuroscience and communication systems.
