Multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions

被引：89
|
作者：
Zhang, Lei [1 ]
Yi, Zhang [1 ]
Yu, Jiali [1 ]
机构：
[1] Univ Elect Sci & Technol China, Sch Engn & Comp Sci, Computat Intelligence Lab, Chengdu 610054, Peoples R China
来源：
IEEE TRANSACTIONS ON NEURAL NETWORKS | 2008年 / 19卷 / 01期
基金：
中国国家自然科学基金; 高等学校博士学科点专项科研基金;
关键词：
attractivity; boundedness; invariant sets; local inhibition; multiperiodicity; periodic trajectory;
D O I：
10.1109/TNN.2007.904015
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
This paper studies multiperiodicity and attractivity for a class of recurrent neural networks (RNNs) with unsaturating piecewise linear transfer functions and variable delays. Using local inhibition, conditions for boundedness and global attractivity are established. These conditions allow coexistence of stable and unstable trajectories. Moreover, multiperiodicity of the network is investigated by using local invariant sets. It shows that under some interesting conditions, there exists one periodic trajectory in each invariant set which exponentially attracts all trajectories in that region correspondingly. Simulations are carried out to illustrate the theories.
引用
收藏
页码：158 / 167
页数：10
相关论文
共 50 条
  • [31] Periodically Intermittent Stabilization of Delayed Neural Networks Based on Piecewise Lyapunov Functions/Functionals
    Chen, Wu-Hua
    Zhong, Jiacheng
    Jiang, Zhiyong
    Lu, Xiaomei
    [J]. CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 2014, 33 (12) : 3757 - 3782
  • [32] Multistability and Instability of Neural Networks With Discontinuous Nonmonotonic Piecewise Linear Activation Functions
    Nie, Xiaobing
    Zheng, Wei Xing
    [J]. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2015, 26 (11) : 2901 - 2913
  • [33] The multistability of delayed competitive neural networks with piecewise non-monotonic activation functions
    Zhang, Yan
    Qiao, Yuanhua
    Duan, Lijuan
    Miao, Jun
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (16) : 10295 - 10311
  • [34] Non-uniform Piecewise Linear Activation Functions in Deep Neural Networks
    Zhu, Zezhou
    Dong, Yuan
    [J]. 2022 26TH INTERNATIONAL CONFERENCE ON PATTERN RECOGNITION (ICPR), 2022, : 2107 - 2113
  • [35] Periodically Intermittent Stabilization of Delayed Neural Networks Based on Piecewise Lyapunov Functions/Functionals
    Wu-Hua Chen
    Jiacheng Zhong
    Zhiyong Jiang
    Xiaomei Lu
    [J]. Circuits, Systems, and Signal Processing, 2014, 33 : 3757 - 3782
  • [36] Local Stability Analysis of High-Order Recurrent Neural Networks with Multi-Step Piecewise Linear Activation Functions
    Huang, Yujiao
    Zhang, Huaguang
    Yang, Dongsheng
    [J]. PROCEEDINGS OF THE 2013 IEEE SYMPOSIUM ON ADAPTIVE DYNAMIC PROGRAMMING AND REINFORCEMENT LEARNING (ADPRL), 2013, : 1 - 5
  • [37] Stability of Stochastic Recurrent Neural Networks with Positive Linear Activation Functions
    Liao, Wudai
    Yang, Xuezhao
    Wang, Zhongsheng
    [J]. ADVANCES IN NEURAL NETWORKS - ISNN 2009, PT 1, PROCEEDINGS, 2009, 5551 : 279 - +
  • [38] Learning continuous piecewise non-linear activation functions for deep neural networks
    Gao, Xinchen
    Li, Yawei
    Li, Wen
    Duan, Lixin
    Van Gool, Luc
    Benini, Luca
    Magno, Michele
    [J]. 2023 IEEE INTERNATIONAL CONFERENCE ON MULTIMEDIA AND EXPO, ICME, 2023, : 1835 - 1840
  • [39] Multistability and Instability of Neural Networks with Non-monotonic Piecewise Linear Activation Functions
    Nie, Xiaobing
    Cao, Linde
    [J]. 2015 SEVENTH INTERNATIONAL CONFERENCE ON ADVANCED COMPUTATIONAL INTELLIGENCE (ICACI), 2015, : 152 - 157
  • [40] Multistability of Memristive Neural Networks with Non-monotonic Piecewise Linear Activation Functions
    Nie, Xiaobing
    Cao, Jinde
    [J]. ADVANCES IN NEURAL NETWORKS - ISNN 2015, 2015, 9377 : 182 - 191
12345