American Institute of Mathematical Sciences

Advanced
July  2004, 10(3): 805-826. doi: 10.3934/dcds.2004.10.805

Asymptotic behaviors in a transiently chaotic neural network

Shyan-Shiou Chen 1, and  Chih-Wen Shih 1,

1. 

Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, Taiwan

Received  January 2002 Revised  May 2003 Published  January 2004

We are interested in the asymptotic behaviors of a discrete-time neural network. This network admits transiently chaotic behaviors which provide global searching ability in solving combinatorial optimization problems. As the system evolves, the variables corresponding to temperature in the annealing process decrease, and the chaotic behaviors vanish. We shall find sufficient conditions under which evolutions for the system converge to a fixed point of the system. Attracting sets and uniqueness of fixed point for the system are also addressed. Moreover, we extend the theory to the neural networks with cycle-symmetric coupling weights and other output functions. An application of this annealing process in solving travelling salesman problems is illustrated.
Keywords: Lyapunov function, Neural network, convergence of dynamics..
Mathematics Subject Classification: 92B20, 39A1.
Citation: Shyan-Shiou Chen, Chih-Wen Shih. Asymptotic behaviors in a transiently chaotic neural network. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 805-826. doi: 10.3934/dcds.2004.10.805
[1]

Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure & Applied Analysis, 2009, 8 (2) : 655-671. doi: 10.3934/cpaa.2009.8.655
[2]

Ying Sue Huang, Chai Wah Wu. Stability of cellular neural network with small delays. Conference Publications, 2005, 2005 (Special) : 420-426. doi: 10.3934/proc.2005.2005.420
[3]

King Hann Lim, Hong Hui Tan, Hendra G. Harno. Approximate greatest descent in neural network optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 327-336. doi: 10.3934/naco.2018021
[4]

Ndolane Sene. Fractional input stability and its application to neural network. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 853-865. doi: 10.3934/dcdss.2020049
[5]

Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367
[6]

Hui-Qiang Ma, Nan-Jing Huang. Neural network smoothing approximation method for stochastic variational inequality problems. Journal of Industrial & Management Optimization, 2015, 11 (2) : 645-660. doi: 10.3934/jimo.2015.11.645
[7]

Yixin Guo, Aijun Zhang. Existence and nonexistence of traveling pulses in a lateral inhibition neural network. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1729-1755. doi: 10.3934/dcdsb.2016020
[8]

Jianhong Wu, Ruyuan Zhang. A simple delayed neural network with large capacity for associative memory. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 851-863. doi: 10.3934/dcdsb.2004.4.851
[9]

Sanjay K. Mazumdar, Cheng-Chew Lim. A neural network based anti-skid brake system. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 321-338. doi: 10.3934/dcds.1999.5.321
[10]

K. L. Mak, J. G. Peng, Z. B. Xu, K. F. C. Yiu. A novel neural network for associative memory via dynamical systems. Discrete & Continuous Dynamical Systems - B, 2006, 6 (3) : 573-590. doi: 10.3934/dcdsb.2006.6.573
[11]

Honggang Yu. An efficient face recognition algorithm using the improved convolutional neural network. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 901-914. doi: 10.3934/dcdss.2019060
[12]

Lidong Liu, Fajie Wei, Shenghan Zhou. Major project risk assessment method based on BP neural network. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1053-1064. doi: 10.3934/dcdss.2019072
[13]

Zhuwei Qin, Fuxun Yu, Chenchen Liu, Xiang Chen. How convolutional neural networks see the world --- A survey of convolutional neural network visualization methods. Mathematical Foundations of Computing, 2018, 1 (2) : 149-180. doi: 10.3934/mfc.2018008
[14]

Wilhelm Schlag. Regularity and convergence rates for the Lyapunov exponents of linear cocycles. Journal of Modern Dynamics, 2013, 7 (4) : 619-637. doi: 10.3934/jmd.2013.7.619
[15]

Leong-Kwan Li, Sally Shao. Convergence analysis of the weighted state space search algorithm for recurrent neural networks. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 193-207. doi: 10.3934/naco.2014.4.193
[16]

Regina S. Burachik, C. Yalçın Kaya. An update rule and a convergence result for a penalty function method. Journal of Industrial & Management Optimization, 2007, 3 (2) : 381-398. doi: 10.3934/jimo.2007.3.381
[17]

Proscovia Namayanja. Chaotic dynamics in a transport equation on a network. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3415-3426. doi: 10.3934/dcdsb.2018283
[18]

Peter Giesl. Construction of a global Lyapunov function using radial basis functions with a single operator. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 101-124. doi: 10.3934/dcdsb.2007.7.101
[19]

Andrei Korobeinikov, Philip K. Maini. A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence. Mathematical Biosciences & Engineering, 2004, 1 (1) : 57-60. doi: 10.3934/mbe.2004.1.57
[20]

Łukasz Struski, Jacek Tabor. Expansivity implies existence of Hölder continuous Lyapunov function. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3575-3589. doi: 10.3934/dcdsb.2017180

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (6)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences