Related Research On Memristor-based Fractional-order Neural Networks

Several dynamic matters of the memristor-based fractional-order neural networks with time delay have been investigated in this article.Through constructing proper Lyapunov function and applying appropriate inequalities,the stability and dissipativity of the addressed neural networks have been analyzed and several sufficient conditions also derived.In addition,via combining the stability theory with adaptive controllers,sufficient conditions that ensure the projective synchronization of the systems have also been established.Based on MATLAB programming,the validity and feasibility of our theoretical results have been demonstrated by numerical simulations.Five chapters make up the paper and the corresponding descriptions are given as follows.Chapter 1 is the introduction.In the first place,the formation and development of the fractional-order neural networks are introduced.Secondly,the characteristics of the memristor are presented and the current situation of memristor-based neural networks is illustrated.Last but not least,memristor-based fractional-order neural networks are introduced as well.Furthermore,some fundamental mathematical definitions and tools,which will be utilized in the later part of our paper,are exhibited.In the second chapter,a class of memristor-based fractional-order neural networks is studied.By adopting contraction mapping principle,sufficient conditions that ensure the existence and uniqueness of the equilibrium point is developed.Via constructing Lyapunov function and applying the Gronwall integral inequality,new criteria that guarantee the global Mittag-leffler stability of the addressed neural networks are proposed.In the third chapter,a class of memristor-based fractional-order bidirectional associative memory neural networks is investigated.As for this kind of neural networks,by virtue of fractional Halanay inequality and fractional comparison principle,the dissipativity of the system is analyzed.Moreover,a global attractive set of the system is clearly clarified.In the fourth chapter,a class of memristor-based fractional-order complex-valued neural networks is discussed.Different from the former chapters,the existence and uniqueness of the equilibrium point in this chapter is proved by homeomorphism theory and M-matrix theory.Moreover,the asymptotic stability of the system is demonstrated via applying fractional Halanay inequality.In addition,two adaptive controllers are designed and Lyapunov-like functions are constructed to illustrate the projective synchronization of the addressed systems.In the fifth chapter,the whole work of this article is summarized and the possible research directions in the future are pointed out as well.