Dynamic Study Of Memristor-based Complex-Valued Neural Networks

Since the concept of memristor was proposed by Chua in 1971 as well as the practical device was successfully developed by Hewlett-Packard in 2008,memristor-based neural networks have attracted much attention from researchers.With the in-creasing demands in various fields,for some problems under the complex number fields,memristor-based real-valued neural networks can not be a useful tool to solve these problems.Thus,memristor-based complex-valued neural networks have been proposed,the dynamic study of memrsitor-based complex-valued neural networks has became one of the hottest topics in recent years.By constructing the appropriate Lyapunov function or functional,using the the-ory of set-valued map and some inequality technique,this paper studies the dynamic of memristor-based complex-valued neural networks.That includes the input-to-state stability,synchronization control and anti-synchronization control of memristor-based complex-valued neural networks with time delays.Through studying the dynamic of memristor-based complex-valued neural networks,some preliminary theoretical results have been obtained.The specific works of this paper as follows:Chapter 1 introduces the concept and research significance of memristor.After that the research status of memristor-based real-valued neural networks and memristor-based complex-valued neural networks are summarized,respectively.Finally,some necessarily propaedeutics and the main investigated contents of this paper are given.Chapter 2 discusses the input-to-state stability of the memristor-based complex-valued neural networks with time delays,some algebraic criteria are obtained for guar-anteeing the input-to-state stability of the considered systems.Chapter 3 investigates the synchronization of memristor-based complex-valued delayed neural networks based on the derive-response concept.Under the linear s-tate feedback control,algebraic conditions are given to ascertain drive system anti-synchronize with response system.Chapter 4 studies the anti-synchronization control problem of memristor-based complex-valued delayed neural networks.By constructing Lyapunov functional and using some inequality techniques,several algebraic conditions are obtained to ensure anti-synchronization between drive system and response system.The effectiveness of the obtained theoretical results is verified by numerical simulations.Finally,Chapter 5 summarizes the research conclusions and points out the prob-lems to be further research in the future.