The Study On The Dynamical Behaviors In Periodic Solution Of Memristor-based Neural Networks With Time-Varying Delays

In recent years, memristor-based neural networks have been widespread attention to domestic and international scholars, especially with the study on periodic solution of memristor-based neural networks with time-varying delays, which is important direction in neural networks research. This dissertation has conducted the research focusing on a large number of fields, especially with automatic control, combinatorial optimization, pattern recognition, image processing. However, with the social development and progress, the study of periodic solution of memristor-based neural networks need to be more thorough and meticulous. This paper use Yoshizawa-like theorem and Kakutani fixed theorem to study periodic solution of memristor-based neural networks with time-varying delays.The existence, global exponential stability, and global exponential dissipativity of periodic solutions are investigated. Its main contents can be summarized as follows:1. In the first part, we mainly discuss a class of memristor-based BAM neural networks with time-varying delays. By applying the theorem of set-valued maps, Chain rule,Yoshizawa-like theorem and inequalities technique, to ensure the uniqueness and existence of periodic solution. Further, by using functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring global exponential stability of periodic solution of memristor-based BAM neural networks. Finally, Numerical simulations are carried out to demonstrate the feasibility of the main results.2. In the second part, memristor-based neural networks with mixed delays is proposed, based on the framework of Filippov solutions, functional differential inclusions theorem and Kakutani fixed theorem are successfully applies to obtain the existence of periodic solution of memristor-based neural networks with mixed delays. Besides, some sufficient conditions are given to guarantee global exponential dissipativity of memristorbased neural networks with mixed delays. Finally, two examples with numerical simulations are given to demonstrate the effectiveness of the obtained results.