兩類細胞神經網絡周期解的存在性與全局指數(shù)穩(wěn)定性.pdf

1、南京航空航天大學碩士學位論文兩類細胞神經網絡周期解的存在性與全局指數(shù)穩(wěn)定性姓名：周平平申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：陳芳啟20081201兩類細胞神經網絡周期解的存在性與全局指數(shù)穩(wěn)定性 iiAbstract At present, cellular neural networks, especially the research of the periodic solutions, have become a hot res

2、earch topic in the field of mathematics. It’s well know that the periodic phenomenon exists generally in the natural world. For instance, lots of biologic systems lie in the environment of periodic variation and many dyn

3、amics have the periodic characteristics. Some applications in the fields of cell neural networks demand that the networks search the only goal rapidly. Considering the convergence rate, the unique balance point of global

4、 exponential stabilization is requested in the networks. So it is important to study the existence and global exponential stability of periodic solutions for cellular neural networks. In this paper, we discuss the existe

5、nce and global exponential stability of periodic solutions for two classes of cellular neural networks, respectively. First, a class of Cohen-Grossberg neural networks with time-varying delays is studied. Assume that the

6、 behaved functions, amplification functions, and the activation functions satisfy the linear restrictions, we propose some new sufficient conditions which guarantee the existence of periodic solutions, by using the Mawhi

7、n’s continuation theorem for coincidence degree and some inequality analysis techniques. Based on Lyapunov functional method, the global exponential stability of periodic solutions for this class of neural networks is pr

8、esented. Then, we discuss a class of bidirectional associative memory neural networks with distributed delays. Under the conditions of the state functions satisfying the linear restrictions, the existence and global expo

9、nential stability of periodic solutions for this class of neural networks are given, by using the Mawhin’s continuation theorem and proper Lyapunov function. The results of this thesis are better than those existed alrea