Generalized Synchronization and Bistability in Chaotic Systems via Decaying Poincaré-Activated Coupling

This study presents an energy-efficient unidirectional coupling strategy for achieving Generalized Synchronization (GS) and bistability in chaotic systems. The method generates decaying coupling signals activated by Poincaré plane crossings of the drive system’s trajectory. Unlike traditional constant coupling, the signal amplitude decays exponentially between crossings, reducing energy consumption while maintaining synchronization. The coupling combines (i) decaying signals activated by Poincaré crossings and (ii) continuous negative feedback from the response/auxiliary systems. Applied to identical pairs of Rössler and Lorenz systems, the method achieves GS and induces identical or indirect synchronization between response and auxiliary systems. The results demonstrate advantages over classical schemes, including lower energy requirements and complex dynamical behaviors. This work advances energy-efficient coupling strategies for chaotic systems, with potential applications in low-power electronics and biological-inspired systems.