μ-synchronization of coupled neural networks with hybrid delayed and non-delayed impulsive effects

In this study, the μ-synchronization challenges posed by coupled neural networks with a combination of delayed and non-delayed impulsive effects are thoroughly investigated. The time delays present in the system are assumed to be unbounded and non-differentiable. A novel impulsive differential inequality is derived, which extends the well-established Halanay type inequality, to analyze the μ-synchronization of coupled neural networks with hybrid impulses. Utilizing the principles of μ-stability theory, several synchronization criteria are derived to ensure the synchronization of the concerned neural networks. The results of this study demonstrate that both non-delayed and delayed impulsive effects have a positive impact on the synchronization process and can be regarded as synchronizing impulses. Additionally, this paper eliminates the limitation on the lower bound of the impulsive interval imposed by time delays. Finally, numerical simulations are carried out to validate our theoretical results, and an example of image encryption is demonstrated as a practical application of the derived results.