Dynamical Behavior of Complex-Valued Hopfield Neural Networks with Discontinuous Activation Functions
作者: Zengyun WangZhenyuan GuoLihong HuangXinzhi Liu
作者单位: 1Hunan First Normal University
2University of Waterloo
3Hunan University
4Changsha University of Science and Technology
刊名: Neural Processing Letters, 2017, Vol.45 (3), pp.1039-1061
来源数据库: Springer Nature Journal
DOI: 10.1007/s11063-016-9563-5
关键词: Discontinuous complex-valued Hopfield neural networkGlobal stabilityConvergence in finite timeDifferential inclusionFilippov solution
原始语种摘要: This paper presents some theoretical results on dynamical behavior of complex-valued neural networks with discontinuous neuron activations. Firstly, we introduce the Filippov differential inclusions to complex-valued differential equations with discontinuous right-hand side and give the definition of Filippov solution for discontinuous complex-valued neural networks. Secondly, by separating complex-valued neural networks into real and imaginary part, we study the existence of equilibria of the neural networks according to Leray–Schauder alternative theorem of set-valued maps. Thirdly, by constructing appropriate Lyapunov function, we derive the sufficient condition to ensure global asymptotic stability of the equilibria and convergence in finite time. Numerical examples are given to show...
全文获取路径: Springer Nature  (合作)
影响因子:1.24 (2012)

  • asymptotic 渐近的
  • complex 超群
  • discontinuous 不连续的
  • neural 神经系统的
  • separating 分隔
  • equilibria 平衡
  • constructing 合组
  • valued 贵重的
  • according 按照
  • ensure 担保