Exponential synchronization of delayed fractional complex network with non-instantaneous impulses via aperiodic control

This paper investigates the exponential synchronization of short-memory fractional complex networks with non-instantaneous impulsive effects, where each node is subject to both individual and coupling time-varying delays. First, we formulate the mathematical structure of the complex network by incorporating short-memory fractional dynamics of the nodes and time-varying delays. In addition, we consider two specified intervals of non-instantaneous impulsive disturbances. Second, to enhance the synchronization performance, an aperiodic intermittent control strategy is proposed, which requires control activation only during irregular time intervals. Next, by employing fractional Lyapunov functions together with the Lyapunov-Razumikhin method, we derive several sufficient conditions that guarantee exponential synchronization of the network. Finally, simulations of the fractional-order Hindmarsh-Rose neuron network are performed to support the theoretical results and shows the model effectiveness in capturing complex neural dynamics.