Synchronization of Fractional Reaction-Diffusion Neural Networks With Time-Varying Delays and Input Saturation

This study is concerned with a synchronization problem of two fractional reaction-diffusion neural networks with input saturation and time-varying delays by the Lyapunov direct method. We extend the traditional ellipsoid method by giving the novel definition of the ellipsoid and linear region of the saturated, which makes our method succinct and effective. First, we linearize the saturation terms by the properties of convex hulls. Then, by using a new Lyapunov-Krasovskii functional, we give the synchronization criteria and estimate the domain of attraction. All the results are presented in the form of linear matrix inequalities(LMIs). Finally, two numerical experiments verify the validity and reliability of our method.

Automated summary

This study addresses the synchronization problem of two fractional reaction-diffusion neural networks with input saturation and time-varying delays using the Lyapunov direct method. By introducing a novel definition of the ellipsoid and linear region of the saturated, the traditional ellipsoid method is extended, making the approach concise and effective. Through the utilization of a new Lyapunov-Krasovskii functional, synchronization criteria are established and the domain of attraction is estimated, with all results presented in the form of linear matrix inequalities (LMIs).