Delayed Pinning Impulsive Synchronization of Coupled Delayed Memristive Neural Networks on Time Scales

ABSTRACT

This paper investigates the synchronization problem of coupled delayed memristive neural networks on time scales. To address the limitations of traditional studies, where continuous‐time and discrete‐time models are treated separately, leading to scattered theoretical tools and difficulties in analysing hybrid‐time systems, the unified modelling framework based on time scales is established, capable of simultaneously describing continuous, discrete and hybrid‐time systems and providing a consistent theoretical basis for synchronization analysis while avoiding redundant derivations. Furthermore, in practical complex networks, signal transmission delays and neuron response lags can significantly affect synchronization performance and conventional impulsive control may fail or be inefficient if these delays are ignored. Therefore, the delayed pinning impulsive control strategy is introduced, in which control inputs are applied to a subset of critical nodes at finite impulsive instants, fully exploiting the propagation characteristics of the network coupling structure to achieve global synchronization with only a few controlled nodes, thereby enhancing control efficiency and reducing control cost. Meanwhile, Lyapunov functions are constructed within the time scale framework to rigorously derive synchronization criteria, ensuring the reliability of the control strategy. Numerical simulations demonstrate that the proposed method effectively achieves synchronization across continuous, discrete and hybrid‐time systems, validating its effectiveness and applicability. Moreover, a perturbation test under the case with 2 pinned nodes is conducted, and the results show that the proposed controller remains effective under admissible perturbations in the initial values and memristive bounds.