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Stability of discrete Hopfield neural networks with delay

Journal of Systems Engineering and Electronics 2005年第4期16卷 937-940页

作者： Ma Runnian 1,2 , Lei Sheping3 & Liu Naigong41. Telecommunication Engineering Inst., Air Force Engineering Univ., Xi’an 710071, P. R. China 2. Key Lab of Information Sciences and Engineering, Dalian Univ., Dalian 111662, P. R. China 3. School of Humanity Law and Economics, Northwestern Polytechnical Univ., Xi’an 710072, P. R. China 4. Science Inst., Air Force Engineering Univ., Xi’an 710051, P. R. China Telecommunication Engineering Inst. Air Force Engineering Univ. XT an 710071 P. R. China Key Lab of Information Sciences and Engineering Dalian Univ. Dalian 111662 P. R. China School of Humanity Law and Economics Northwestern Polytechnical Univ. XT an 710072 P. R. China Science Inst. Air Force Engineering Univ. XT an 710051 P. R. China

Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. As it is well known, the stability of neural networks is not only the most basic and important problem but also foundation of the network＇s applications. The stability of discrete HJopfield neural networks with delay is mainly investigated by using Lyapunov function. The sufficient conditions for the networks with delay converging towards a limit cycle.of length 4 are obtained. Also, some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle.with length 2. The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.

关键词： discrete Hopfield neural network with delay stability limit cycle.

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POSITIVE EQUILIBRIUM AND ITS STABILITY OF THE BEDDINGTON-DEANGELIS'TYPE PREDATOR-PREY DYNAMICAL SYSTEM

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Applied Mathematics(A Journal of Chinese Universities) 2006年第4期21卷 429-436页

作者： Xiao Haibin Department of Mathematics, Ningbo University, Zhejiang 315211,China Department of Mathematics, Nanjing University, Jiangsu 210093,China. Department of Mathematics Ningbo University China Department of Mathematics Nanjing University China

A class of Beddington-DeAngelis＇ type predator-prey dynamic system with prey and predator both having linear density restriction is considered. By using the qualitative methods of ODE, the existence and uniqueness of positive equilibrium and its global asymptotic stability are analyzed. The direct criterions for local stability of positive equilibrium and existence of limit cycle.are also established when inference parameter of predator is small.

关键词： density restriction Beddington-DeAngelis' type functional response global stability limit cycle.

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QUALITATIVE ANALYSIS OF BIOECOLOGY DIFFERENTIAL SYSTEM

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生物数学学报 1993年第2期8卷 1-8页

作者： Gu Daoxiu (Hunan Educational Institute, Changsha 410012, China) 湖南教育所湖南长沙

In this paper, the author studies the quartic bioecology differential system:Here n and q are positive constants, l、m and p are constants. The author also proves some theorems of existence and uniqueness of limit cyc... 详细信息

关键词： Bioecology system singular point characteristic equations limit cycle.

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GLOBAL ANALYSIS OF A CLASS OF CUBIC SYSTEMS

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Annals of Differential Equations 1996年第4期12卷 475-482页

作者：王现南京大学

The paper gives a complete golbal phase plane analysis of the cubic system x = y ax2-dx3,y=-x + bx2 + x3, which arises in the study of the structure of a three-dimensional viscous flow near a plane wall.

关键词： nonlinear system global analysis limit cycle.

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Global bifurcation of a cubic system perturbed by degree four

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上海师范大学学报（自然科学版） 2014年第5期43卷 464-475页

作者： Desheng Shang Zheng Wang Department of Mathematics School of SciencesShandong University of Technology Zibo 255049 China

Using the method of multi-parameter perturbation theory and qualitative analysis,a cubic system perturbed by degree four are investigated in this paper. After systematic analysis,it is found that the studied system ca... 详细信息

关键词： Perturbation Homoclinic orbit Melnikov function bifurcation limit cycle.

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