摘要：
In this paper, the global stability has been investigated for a novel class of competitive neural networks with mixed time delays and discontinuous activations. Without presuming the boundedness of activation functions, we draw two set of sufficient conditions ensuring the existence, uniqueness of the equilibrium, global exponential asymptotic stability of the solution and the associated output of the solution converging to the output equilibrium point in measure, by linear matrix inequality, M-matrix, Leray-Schauder alternative theorem in multivalued analysis, general Lyapunov method, topological degree theory of set-valued map. Meanwhile, we present a result on the global convergence in finite time of given neural networks. The results in the literature are generalized and significantly improved. Finally, one example and simulations are presented to demonstrate the effectiveness of the theoretical results. In this paper, the global stability has been investigated for a novel class of competitive neural networks with mixed time delays and discontinuous activations. Without presuming the boundedness of activation functions, we draw two set of sufficient conditions ensuring the existence, uniqueness of the equilibrium, global exponential asymptotic stability of the solution and the associated output of the solution converging to the output equilibrium point in measure, by linear matrix inequality, M-matrix, Leray-Schauder alternative theorem in multivalued analysis, general Lyapunov method, topological degree theory of set-valued map. Meanwhile, we present a result on the global convergence in finite time of given neural networks. The results in the literature are generalized and significantly improved. Finally, one example and simulations are presented to demonstrate the effectiveness of the theoretical results.
作者机构：
[Huang, Lihong; Wang, Yanqun] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.;[Wang, Yanqun] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421008, Hunan, Peoples R China.;[Huang, Lihong] Hunan Womens Univ, Changsha 410004, Hunan, Peoples R China.
通讯机构：
[Huang, Lihong] H;Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.
关键词：
Discontinuous activation;Generalized Lyapunov-like approach;Global exponential asymptotic stability;Leray-Schauder alternative theorem;Mixed time delays
摘要：
In this paper, we investigate the dynamical behaviors of a novel class of Cohen-Grossberg neural networks with not only mixed time delays, i.e., time varying delays and distributed delays, but also discontinuous activations, which may be unbounded or nonmonotonic. Some sufficient conditions are derived to ensure the existence, uniqueness of the equilibrium, global exponential asymptotic stability of the solution and the associated output of the solution converging to the output equilibrium point in measure by using the Leray-Schauder alternative theorem in multivalued analysis, matrix theory and generalized Lyapunov-like approach. Some recent results in the literature are generalized and significantly improved. One example is provided to demonstrate the effectiveness of the theoretical results. (C) 2013 Elsevier B.V. All rights reserved.
