Projective lag synchronization of fractional delayed memristive neural networks via event-based hybrid pinning impulsive controller

This paper delves into the projective lag synchronization of Riemann–Liouville type fractional-order memristive neural networks accounting for jump mismatch. Recognizing the inherent inconsistencies in synchronizing traditional fractional-order memristive neural networks, we introduce a novel mathematical model that accommodates the jump mismatch phenomenon. A groundbreaking event-based hybrid pinning impulsive controller is then introduced, equipped with tailored event-triggering conditions, to elucidate the global asymptotic projective lag synchronization. Leveraging inequality principles and impulse analysis, a new Lyapunov functional is proposed, formulating sufficient conditions for synchronization while theoretically eliminating Zeno behavior in the controller. Notably, our approach substantially optimizes control overhead while fulfilling practical synchronization requisites. In addition, the obtained sufficient conditions can theoretically guide practical engineering applications of the network. Finally, a simulation example, emphasizing varied projective and lag factors, demonstrates our findings.