American Institute of Mathematical Sciences

Advanced
2007, 2007(Special): 391-398. doi: 10.3934/proc.2007.2007.391

New discrete analogue of neural networks with nonlinear amplification function and its periodic dynamic analysis

Xilin Fu 1, and  Zhang Chen 2,

1. 

School of Mathematical Science, Shandong Normal University, Jinan, Shandong 250014, P.R., China
2. 

School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, P. R., China

Received  September 2006 Revised  June 2007 Published  September 2007

In this paper, new discrete analogue of a class of neural networks with nonlinear amplification function is obtained by analysis and approximation techniques. Using continuation theorem of coincidence degree theory, periodic solution for discrete model is studied, and sufficient condition is given to guarantee the existence of periodic solution. Moreover, global stability on periodic solution is investigated by Lyapunov method.
Keywords: coincidence degree, global exponential stability., Discrete neural networks, time delay, periodic solution.
Mathematics Subject Classification: 39A10, 39A1.
Citation: Xilin Fu, Zhang Chen. New discrete analogue of neural networks with nonlinear amplification function and its periodic dynamic analysis. Conference Publications, 2007, 2007 (Special) : 391-398. doi: 10.3934/proc.2007.2007.391
[1]

Xiang Xie, Honglei Xu, Xinming Cheng, Yilun Yu. Improved results on exponential stability of discrete-time switched delay systems. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 199-208. doi: 10.3934/dcdsb.2017010
[2]

Benedetta Lisena. Average criteria for periodic neural networks with delay. Discrete and Continuous Dynamical Systems - B, 2014, 19 (3) : 761-773. doi: 10.3934/dcdsb.2014.19.761
[3]

Ricai Luo, Honglei Xu, Wu-Sheng Wang, Jie Sun, Wei Xu. A weak condition for global stability of delayed neural networks. Journal of Industrial and Management Optimization, 2016, 12 (2) : 505-514. doi: 10.3934/jimo.2016.12.505
[4]

Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, 2021, 29 (4) : 2599-2618. doi: 10.3934/era.2021003
[5]

Quan Hai, Shutang Liu. Mean-square delay-distribution-dependent exponential synchronization of chaotic neural networks with mixed random time-varying delays and restricted disturbances. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3097-3118. doi: 10.3934/dcdsb.2020221
[6]

Sylvia Novo, Rafael Obaya, Ana M. Sanz. Exponential stability in non-autonomous delayed equations with applications to neural networks. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 517-536. doi: 10.3934/dcds.2007.18.517
[7]

Xiaochen Mao, Weijie Ding, Xiangyu Zhou, Song Wang, Xingyong Li. Complexity in time-delay networks of multiple interacting neural groups. Electronic Research Archive, 2021, 29 (5) : 2973-2985. doi: 10.3934/era.2021022
[8]

Zhigang Zeng, Tingwen Huang. New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays. Journal of Industrial and Management Optimization, 2011, 7 (2) : 283-289. doi: 10.3934/jimo.2011.7.283
[9]

Jianping Zhou, Yamin Liu, Ju H. Park, Qingkai Kong, Zhen Wang. Fault-tolerant anti-synchronization control for chaotic switched neural networks with time delay and reaction diffusion. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1569-1589. doi: 10.3934/dcdss.2020357
[10]

Serge Nicaise, Cristina Pignotti, Julie Valein. Exponential stability of the wave equation with boundary time-varying delay. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 693-722. doi: 10.3934/dcdss.2011.4.693
[11]

Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2677-2692. doi: 10.3934/dcdsb.2020200
[12]

Muhammet Mert Ketencigil, Ozlem Faydasicok, Sabri Arik. Novel criteria for robust stability of Cohen-Grossberg neural networks with multiple time delays. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022081
[13]

Yong Ren, Huijin Yang, Wensheng Yin. Weighted exponential stability of stochastic coupled systems on networks with delay driven by $ G $-Brownian motion. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3379-3393. doi: 10.3934/dcdsb.2018325
[14]

Ling Zhang, Xiaoqi Sun. Stability analysis of time-varying delay neural network for convex quadratic programming with equality constraints and inequality constraints. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022035
[15]

Hal L. Smith, Horst R. Thieme. Persistence and global stability for a class of discrete time structured population models. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4627-4646. doi: 10.3934/dcds.2013.33.4627
[16]

Luis Barreira, Claudia Valls. Delay equations and nonuniform exponential stability. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 219-223. doi: 10.3934/dcdss.2008.1.219
[17]

Meiyu Sui, Yejuan Wang, Peter E. Kloeden. Pullback attractors for stochastic recurrent neural networks with discrete and distributed delays. Electronic Research Archive, 2021, 29 (2) : 2187-2221. doi: 10.3934/era.2020112
[18]

Yaru Xie, Genqi Xu. Exponential stability of 1-d wave equation with the boundary time delay based on the interior control. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 557-579. doi: 10.3934/dcdss.2017028
[19]

Yong Zhao, Qishao Lu. Periodic oscillations in a class of fuzzy neural networks under impulsive control. Conference Publications, 2011, 2011 (Special) : 1457-1466. doi: 10.3934/proc.2011.2011.1457
[20]

Hotaka Udagawa, Taiji Okano, Toshimichi Saito. Permutation binary neural networks: Analysis of periodic orbits and its applications. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022097

 Impact Factor: 

Tools

Metrics

  • PDF downloads (38)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy