| Memristor is one of the four basic circuit elements,it represents the relationship between electric charge and magnetic flux,the resistance of memristors is determined by the electric charge flowing through it.Therefore,memristor is used instead of ordinary resistance.Later,memristor was introduced into neural network to form a new neural network-memristive neural network.The global Mittag-Leffler stability of memristive fractional-order neural networks and the global exponential stabilization of memristive high-order BAM neural networks are investigated in this thesis.It consists of four chapters.The main contents are as follows:The first chapter is the introduction.It describes the research background of this article,at the same time,the dynamic behaviors of memristive fractional-order neural networks and memristive high-order BAM neural networks are summarized.Meanwhile,some symbolic instructions for the whole thesis are given,and the necessary definitions and lemmas are provided.The global Mittag-Leffler stability of memristive fractional-order neural networks is investigated in chapter 2.With the help of contraction mapping principle,a sufficient condition for the existence and uniqueness of the equilibrium point of fractional-order neural networks are obtained.And then,the sufficient condition for global Mittag-Leffler stability of fractionalorder neural networks is gained by constructing a Lyapunov function.In chapter 3,the global exponential stabilization of memristive high-order BAM neural networks is investigated.By using integral inequality,for the delay kernel function,a lemma is proposed,with the help of this lemma,a sufficient condition ensuring the existence and uniqueness of the equilibrium point of the system is obtained.And a new sufficient condition for the global exponential stabilization of the system is gained by constructing a suitable Lyapunov function and controller.The chapter 4,it makes a comprehensive summary of this thesis and gives the content of the research in the future. |
