Multistability and Multiperiodicity for a Class of Cohen–Grossberg BAM Neural Networks with Discontinuous Activation Functions and Time Delays

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• 作者：Yanke Du ; Rui Xu
• 关键词：Multistability ; Multiperiodicity ; Cohen–Grossberg BAM neural network ; Exponential stability ; Discontinuous activation function
• 刊名：Neural Processing Letters
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：42
• 期：2
• 页码：417-435
• 全文大小：937 KB
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• 作者单位：Yanke Du (1)
  Rui Xu (1)
  
  1. Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, People’s Republic of China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Complexity
  Artificial Intelligence and Robotics
  Electronic and Computer Engineering
  Operation Research and Decision Theory
  
• 出版者：Springer Netherlands
• ISSN：1573-773X

文摘

In this paper, a general class of Cohen–Grossberg bidirectional associative memory neural networks (CGBAMNNs) with time-varying delays, distributed delays and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and local exponential stability of multiple equilibrium points, which ensure that \(2n\)-dimensional CGBAMNNs with \(k\)-level discontinuous activation functions can have \(k^n\) equilibrium points. As an extension of multistability, sufficient conditions are obtained to ensure the existence of \(k^n\) locally exponentially stable periodic orbits of the system when time-varying delays and external inputs are periodic. Finally, three examples are given to illustrate the feasibility and application of the obtained results. Keywords Multistability Multiperiodicity Cohen–Grossberg BAM neural network Exponential stability Discontinuous activation function