Complex and chaotic dynamics in a discrete-time-delayed Hopfield neural network with ring architecture

被引:45
作者
Kaslik, Eva [1 ]
Balint, Stefan [1 ]
机构
[1] W Univ Timisoara, Dept Math & Comp Sci, Timisoara 300223, Romania
关键词
Hopfield neural network; Ring architecture; Stability; Bifurcation; Chaos; BIFURCATION-ANALYSIS; NONLINEAR-WAVES; PERIODIC-ORBITS; MULTI-DELAYS; NEURONS; STABILITY; MODEL; SYSTEM; OSCILLATIONS; PATTERNS;
D O I
10.1016/j.neunet.2009.03.009
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 is devoted to the analysis of a discrete-time-delayed Hopfield-type neural network of p neurons with ring architecture. The stability domain of the null solution is found, the values of the characteristic parameter for which bifurcations occur at the origin are identified and the existence of Fold/Cusp, Neimark-Sacker and Flip bifurcations is proved. These bifurcations are analyzed by applying the center manifold theorem and the normal form theory. It is proved that resonant 1:3 and 1:4 bifurcations may also be present. It is shown that the dynamics in a neighborhood of the null solution become more and more complex as the characteristic parameter grows in magnitude and passes through the bifurcation values. A theoretical proof is given for the occurrence of Marotto's chaotic behavior, if the magnitudes of the interconnection coefficients are large enough and at least one of the activation functions has two simple real roots. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1411 / 1418
页数:8
相关论文
共 43 条
[1]   Associative dynamics in a chaotic neural network [J].
Adachi, M ;
Aihara, K .
NEURAL NETWORKS, 1997, 10 (01) :83-98
[2]  
[Anonymous], 1998, ELEMENTS APPL BIFURC, DOI DOI 10.1007/B98848
[3]   HOW DELAYS AFFECT NEURAL DYNAMICS AND LEARNING [J].
BALDI, P ;
ATIYA, AF .
IEEE TRANSACTIONS ON NEURAL NETWORKS, 1994, 5 (04) :612-621
[4]  
Bremen H. F., 1997, PHYSICA D, V101, P1
[5]   Patterns of oscillation in a ring of identical cells with delayed coupling [J].
Bungay, Sharene D. ;
Campbell, Sue Ann .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2007, 17 (09) :3109-3125
[6]   Multistability and stable asynchronous periodic oscillations in a multiple-delayed neural system [J].
Campbell, SA ;
Ncube, I ;
Wu, J .
PHYSICA D-NONLINEAR PHENOMENA, 2006, 214 (02) :101-119
[7]   Qualitative analysis of a neural network model with multiple time delays [J].
Campbell, SA ;
Ruan, SG ;
Wei, JJ .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1999, 9 (08) :1585-1595
[8]  
Chen L, 2001, Dyn Syst Differ Equ, V9, P139
[9]   CHAOTIC SIMULATED ANNEALING BY A NEURAL-NETWORK MODEL WITH TRANSIENT CHAOS [J].
CHEN, LN ;
AIHARA, K .
NEURAL NETWORKS, 1995, 8 (06) :915-930
[10]   Chaos and asymptotical stability in discrete-time neural networks [J].
Chen, LN ;
Aihara, K .
PHYSICA D-NONLINEAR PHENOMENA, 1997, 104 (3-4) :286-325