Global Exponential Stability and Synchronization for Novel Complex-Valued Neural Networks With Proportional Delays and Inhibitory Factors

In this article, complex-valued neural networks (CVNNs) with proportional delays and inhibitory factors are proposed. First, the global exponential stability of the model addressed is investigated by employing the Halanay inequality technique and the matrix measure method. Some criteria are derived to guarantee the global exponential stability of CVNNs with proportional delays and inhibitory factors. The obtained criteria are applicable not only to systems with proportional delays but also to systems with arbitrary delays. Here, the Lyapunov functions are not constructed. Compared with the Lyapunov method, the matrix measure method makes the obtained criteria more concise, and the Halanay inequality makes the analytical procedure more compact. Furthermore, the global exponential synchronization of two neural-network models with proportional delays and inhibitory factors is also studied. By designing a feedback controller and giving some limitation conditions, the drive system and the response system realize global exponential synchronization. Finally, numerical simulation examples are provided to validate the effectiveness of the theoretical results obtained.

Automated summary

This article proposes a complex-valued neural network model with proportional delays and inhibitory factors, and derives criteria for ensuring its global exponential stability using the Halanay inequality technique and matrix measure method. By designing a feedback controller and providing limitation conditions, global exponential synchronization of two neural network models is achieved successfully.