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    题名: On periodic solutions of a two-neuron network system with sigmoidal activation functions
    作者: Hsu, Cheng-hsiung;Yang, Suh-yuh;Yang, Ting-hui;Yang, Tzi-sheng
    贡献者: 淡江大學數學學系
    关键词: Neural networks;periodic solutions;Poincaré–Bendixson theorem;Dulac's criterion;Liapunov functions;contraction mapping theorem
    日期: 2006-05-01
    上传时间: 2011-05-20 09:41:54 (UTC+8)
    出版者: World Scientific Publishing
    摘要: In this paper we study the existence, uniqueness and stability of periodic solutions for a two-neuron network system with or without external inputs. The system consists of two identical neurons, each possessing nonlinear feedback and connected to the other neuron via a nonlinear sigmoidal activation function. In the absence of external inputs but with appropriate conditions on the feedback and connection strengths, we prove the existence, uniqueness and stability of periodic solutions by using the Poincaré–Bendixson theorem together with Dulac's criterion. On the other hand, for the system with periodic external inputs, combining the techniques of the Liapunov function with the contraction mapping theorem, we propose some sufficient conditions for establishing the existence, uniqueness and exponential stability of the periodic solutions. Some numerical results are also provided to demonstrate the theoretical analysis.
    關聯: International Journal of Bifurcation and Chaos 16(5), pp.1405-1417
    DOI: 10.1142/S0218127406015386
    显示于类别:[數學學系暨研究所] 期刊論文

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