Further on Novel Multi-State Coupling and Proportional Distributed Delays in Synchronization of Uncertain Complex-Valued State-Dependent Neural Networks for Secure Communication

This paper investigates the global polynomial synchronization (GPS) of a class of uncertain complex-valued state-dependent neural networks (CVSDNNs) with proportional delays and multi-state coupling via an adaptive event-triggered controller. This work further investigates the synchronization of neural networks (NNs) with proportional distributed delays, as well as the first analysis based on a multi-state coupled NNs (CNNs) model. To effectively handle the challenges posed by proportional distributed delays, we establish two novel integral inequalities developed by exploiting the properties of both the proportional delays and polynomial functions, and construct an appropriate Lyapunov functional. Subsequently, the Intermediate Value Theorem is employed to prove that the Zeno behavior is precluded under the proposed synchronization control. Finally, numerical simulations are conducted not only to validate the theoretical results but also to demonstrate applications in secure communication.