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：
Activation analysis;Asymptotic stability;Chemical activation;Linear matrix inequalities;Lyapunov methods;Set theory;Time delay;Time varying control systems;Time varying networks;Topology;Competitive neural network;Convergence in finite time;Exponential asymptotic stabilities;Global exponential stability;Global stability analysis;Leray-Schauder alternative;Mixed time-varying delays;Topological degree theory;Neural networks;Article;artificial neural network;calculation;competitive neural network;conceptual framework;discontinuous neuron activation;global stability analysis;Leray Schauder alternative theorem in multivalued analysis;linear matrix inequality;Lyapunov method;mathematical analysis;mathematical computing;mixed time varying delay;simulation;statistical analysis;statistical concepts;time series analysis;topological degree theory of set valued map;variance
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.
