数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1192-1204.

• 论文 • 上一篇    

具有不连续激活函数的复数神经网络的全局指数周期性

邹瑶1, 曾春娜2, 胡进1   

  1. 1 重庆交通大学数学与统计学院 重庆 400074;
    2 重庆师范大学数学科学学院 重庆 401331
  • 收稿日期:2018-10-31 修回日期:2018-11-25 发布日期:2019-11-08
  • 通讯作者: 胡进 E-mail:jhu@cqjtu.edu.cn
  • 作者简介:邹瑶,E-mail:18323190385@163.com;曾春娜,E-mail:zengchn@163.com
  • 基金资助:
    国家自然科学基金(61773004,11801048)、重庆高校创新团队建设计划资助项目(CXTDX201601022)、重庆市基础科学与前沿技术研究资助项目(cstc2017jcyjAX0172,cstc2017jcyjAX0022,cstc2017jcyjAX0082,cstc2018jcyjAX0606),重庆市教委科学技术研究资助项目(KJ1705118,KJQN201800740)和重庆市留学人员回国创业创新支持计划(cx2018034)

Global Exponential Periodicity of Complex-Valued Neural Networks with Discontinuous Activation Functions

Zou Yao1, Zeng Chunna2, Hu Jin1   

  1. 1 School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074;
    2 School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
  • Received:2018-10-31 Revised:2018-11-25 Published:2019-11-08
  • Supported by:
    Supported by the NSFC (61773004, 11801048), the Program of Chongqing Innovation Team Project in University (CXTDX201601022), the Natural Scinece Foundation Project of CQ CSTC (cstc2017jcyjAX0172, cstc2017jcyjAX0022, cstc2017jcyjAX0082, cstc2018jcyjAX0606), the Technology Research Foundation of Chongqing Educational Committee (KJ1705118, KJQN201800740) and the Venture & Innovation Support Program for Chongqing Overseas Returnees (cx2018034)

摘要: 具有不连续激活函数的神经网络是一类非常重要的神经网络模型.虽然对具有不连续激活函数的实数神经网络已经有了非常深入的研究,但是对相应的复数神经网络研究成果还不太多.该文利用Filippov微分包含理论,Leray-Schauder替换定理以及Lyapunov函数,对一类具有不连续激活函数的复数神经网络进行了研究,给出了神经网络周期解全局指数稳定的充分条件,最后给出具有仿真的数值例子验证了结果的有效性.

关键词: 不连续激活函数, 复数神经网络, 周期性

Abstract: In this paper, we investigate a type of complex-valued neural networks with discontinuous activation functions. By using Filippov differential inclusion theory, Leray-Schauder alternative theorem and Lyapunov function, we obtain the sufficiet conditions for the global exponential periodicity of the neural network. The simulation shows the effectiveness of the results.

Key words: Complex-valued neural networks, Discontinuous activation functions, Global exponential periodicity

中图分类号: 

  • O175.13