Nonseparation Method-Based Finite/Fixed-Time Synchronization of Fully Complex-Valued Discontinuous Neural Networks

This article mainly focuses on the problem of synchronization in finite and fixed time for fully complex-variable delayed neural networks involving discontinuous activations and time-varying delays without dividing the original complex-variable neural networks into two subsystems in the real domain. To avoid the separation method, a complex-valued sign function is proposed and its properties are established. By means of the introduced sign function, two discontinuous control strategies are developed under the quadratic norm and a new norm based on absolute values of real and imaginary parts. By applying nonsmooth analysis and some novel inequality techniques in the complex field, several synchronization criteria and the estimates of the settling time are derived. In particular, under the new norm framework, a unified control strategy is designed and it is revealed that a parameter value in the controller completely decides the networks are synchronized whether in finite time or in fixed time. Finally, some numerical results for an example are provided to support the established theoretical results.

Automated summary

This article addresses the synchronization issue in finite and fixed time for fully complex-variable delayed neural networks with discontinuous activations and time-varying delays. By introducing a complex-valued sign function and developing two discontinuous control strategies, synchronization criteria and estimates of settling time are derived using nonsmooth analysis and novel inequality techniques in the complex field. The unified control strategy designed under a new norm framework reveals that a parameter value in the controller determines whether the networks synchronize in finite or fixed time, supported by numerical results for an example provided in the article.