Event-triggered synchronization of a two-layer heterogeneous neural network via hybrid control

Multi-layer network contains multiple subsystems and different types of interaction, which is more practical than traditional single-layer network. On this observation, this paper explores point-to-point quasi-synchronization in a two-layer heterogeneous neural network system. The sufficient conditions for global exponential synchronization in the driving layer are given a coupling term. Based on the global exponential synchronization in the driver layer, this paper further studies the global point-to-point quasi-synchronization between the driver layer and the response layer of the two-layer neural network under the hybrid control and event-triggered control. Under this hybrid control strategies, the event can be activated if and only if the trigger condition is violated and the dynamical adaptive control is also involved. Moreover, the Zeno behavior under this strategy is eliminated by Lyapunov method and matrix theory. Finally, a numerical example is given to verify the theoretical results. •Point-to-point synchronization of two-layer heterogeneous neural network is studied.•The intermittent adaptive pinning control and event-triggered control are combined.•Zeno behavior is excluded for hybrid event-triggered protocols.•Sufficient conditions for point-to-point quasi-synchronization are given.