Stability and bifurcation of a Cohen-Grossberg neural network with discrete delays

Applied Mathematics and Computation

Volumn 218, Issue 6, 2011, Pages 2850-2862

  Liu, Qiming ^a   Xu, Rui ^a  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

Cohen Grossberg neural networks; Discrete delay; Hopf bifurcation; Periodic solution; Stability

Indexed keywords

BIFURCATING PERIODIC SOLUTIONS; BIFURCATION PARAMETER; CENTER MANIFOLD THEOREM; COHEN-GROSSBERG NEURAL NETWORKS; DISCRETE DELAY; DISCRETE TIME DELAY; NORMAL FORM THEORY; PERIODIC SOLUTION; QUALITATIVE ANALYSIS; STABILITY AND BIFURCATION;

CONVERGENCE OF NUMERICAL METHODS; NEURAL NETWORKS; PROBLEM SOLVING; UNMANNED AERIAL VEHICLES (UAV);

HOPF BIFURCATION;

EID: 80053286379     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.08.029     Document Type: Article

References (29)

1. M. Cohen, and S. Grossberg Absolute stability and global pattern formation and parallel memory storage by competitive neural networks IEEE Trans. Syst. Man Cybernet. Smc-13 1983 815 826
2. S. Townley, S. Ilchmann, and A. Weiss Existence and learning of oscillations in recurrent neural networks IEEE Trans. Neural Netw. 11 2000 205 214 (Pubitemid 32132901)
3. Z. Huang, and Y. Xia Exponential periodic attractor of impulsive BAM networks with finite distributed delays Chaos Solitons Fract. 39 2009 373 384
4. M. Luo, S. Zhang, R. Wang, and W. Kang Robust stability analysis for discrete-time stochastic neural networks systems with time-varying delays Appl. Math. Comput. 209 2009 305 313
5. Y. Zhang, D. Yue, and E. Tian New stability criteria of neural networks with interval time-varying delay: a piecewise delay method Appl. Math. Comput. 208 2009 248 259
6. Z. Guo, and L. Huang LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations Appl. Math. Comput. 215 2009 889 900
7. C. Bai Stability analysis of Cohen-Grossberg BAM neural networks with delays and impulses Chaos Solitons Fract. 35 2008 263 267 (Pubitemid 47391245)
8. W. Lua, and T. Chen R + n -global stability of a Cohen-Grossberg neural network system with nonnegative equilibria Neural Netw. 20 2007 714 722 (Pubitemid 47239380)
9. X. Yang, X. Liao, C. Li, and Y. Tang Local stability and attractive basin of Cohen-Grossberg neural networks Nolinear Anal.: Real Word Appl. 10 2009 2834 2841
10. Q. Liu Periodic solutions of high-order Cohen-Grosserg neural networks with time-varying delays Adv. Differ. Eqn. Process. 6 1 2010 1 14
11. K. Li, L. Zhang, X. Zhang, and Z. Li Stability in impulsive Cohen-Grossberg-type BAM neural networks with distributed delays Appl. Math. Comput. 215 2010 3970 3984
12. X. Li Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays Appl. Math. Comput. 215 2009 292 307
13. Z. Chen, D. Zhao, and X. Fu Discrete analogue of high-order periodic Cohen-Grossberg neural networks with delay Appl. Math. Comput. 214 2009 210 217
14. Y. Li, X. Chen, and L. Zhao Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on timescales Neurocomputing 72 2009 1621 1630
15. H. Xiang, and J. Cao Exponential stability of periodic solution to Cohen-Grossberg-type BAM networks with time-varying delays Neurocomputing 72 2009 1702 1711
16. S. Ruan, and J. Wei On the zeros of transcendental functions with applications to stability of delay differential equations with two delays Dyn. Continuous Discrete Impuls. Syst. Ser. A 10 2003 867 874
17. J. Wei, and S. Ruan Stability and bifurcation in a neural network model with two delays Physica D 130 1999 255 272 (Pubitemid 129587672)
18. J. Cao, and M. Xiao Stability and Hopf bifurcation in a simplified BAM neural network with two time delays IEEE Trans. Neural Netw. 18 2007 416 430 (Pubitemid 46522566)
19. S. Guo, L. Huang, and L. Wang Lineartability and Hopf bifurcation in a two-neuron network with three delays Int. J. Bifurcat. Chaos 14 2004 2799 2810 (Pubitemid 39326275)
20. C. Huang, L. Huang, J. Feng, M. Nai, and Y. He Hopf bifurcation analysis for a two-neuron network with four delays Chaos Solitons Fract. 34 2007 795 812 (Pubitemid 46601894)
21. X. Zhou, Y. Wu, Y. Li, and X. Yao Stability and bifurcation analysis on a two-neuron networks with discrete and distributed delays Chaos Solitons Fract. 40 2009 1493 1505
22. Y. Yang, and J. Ye Stability and bifurcation in a simplified five-neuron BAM neural networks with delays Chaos Solitons Fract. 42 2009 2357 2363
23. Y. Song, M. Han, and J. Wei Stability and Hopf bifurcation analysis on a simplified BAM neural networks with delays Physica D 200 2005 185 204
24. H. Zhao, and L. Wang Stability and bifurcation for discrete-time Cohen-Grossberg neural networks Appl. Math. Comput. 179 2006 787 798 (Pubitemid 44301460)
25. H. Zhao, and L. Wang Hopf bifurcation in Cohen-Grossberg neural network with distributed delays Nonlinear Anal.: Real World Appl. 8 2007 73 89 (Pubitemid 44584785)
26. J.K. Hale Theory of Functional Differential Equations 1977 Springer New York
27. B.D. Hassard, N.D. Kazarinoff, and Y.H. Wan Theory and Application of Hopf Bifurcation 1981 Cambridge University Press Cambridge
28. Brian F. Redmond Bifurcation Analysis of a Class of Delay-Differential Equation with Reflectional Symmetry: Applications to Enso p. 43 2002 University of Ottawa Canada
29. J. Hamphshire, and A. Waibel A novel objective function for improved pheneme recognition using time-delay neural networks IEEE Trans. Neural Netw. 1 2 1990 216 228 (Pubitemid 20713333)