Optimized multi-variable coupling can improve synchronization in complex networks

Investigating synchronization in networks of oscillators elucidates the intricate interplay between individual dynamics and emergent collective behavior. This study introduces an optimization algorithm to achieve multi-variable coupling for enhancing synchronization in networks of chaotic systems with diffusive couplings. Our results demonstrate that the optimized multi-variable coupling surpasses single-variable and diagonal couplings in achieving synchronization under equivalent total coupling strength. Employing the optimization algorithm, based on the master stability function (MSF), across networks of chaotic Rössler, Hindmarsh-Rose, Lorenz, and Chen reveals that the optimized multi-variable coupling requires lower coupling strength for synchronization than other coupling schemes. Furthermore, the resulting MSF with optimized multi-variable coupling results in more negative values, indicating a higher degree of stability in synchronization.