Stability and Hopf bifurcation analysis on a two-neuron network with discrete and distributed delays

Chaos, Solitons and Fractals

Volumn 40, Issue 3, 2009, Pages 1493-1505

  Zhou, Xiaobing ^a   Wu, Yue ^a   Li, Yi ^a   Yao, Xun ^b  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

[No Author keywords available]

Indexed keywords

NEURAL NETWORKS;

BIFURCATING PERIODIC SOLUTIONS; BIFURCATION PARAMETER; CHARACTERISTIC EQUATION; DIRECTION OF HOPF BIFURCATIONS; DISCRETE AND DISTRIBUTED DELAYS; DISCRETE TIME DELAY; HOPF BIFURCATION ANALYSIS; LOCAL STABILITY;

HOPF BIFURCATION;

EID: 65449179211     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.09.034     Document Type: Article

References (24)

1. Wu J. Introduction to neural dynamics and signal transmission delay (2001), Walter de Gruyter, Berlin
2. Arik S. Global robust stability analysis of neural networks with discrete time delays. Chaos, Solitons & Fractals 26 (2005) 1407-1414
3. Song Y., Han M., and Wei J. Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays. Physica D 200 (2005) 185-204
4. Gilli M. Strange attractors in delayed cellular neural networks. IEEE Trans Circ Syst I 40 (1993) 849-853
5. Gopalsamy K., and Leung I. Delay induced periodicity in a neural netlet of excitation and inhibition. Physica D 89 (1996) 395-426
6. Chen Y., and Wu J. Slowly oscillating periodic solutions for a delayed frustrated network of two neurons. J Math Anal Appl 259 (2001) 188-208
7. Zhou S., Liao X., Yu J., and Wong K.W. Chaos and its synchronization in two-neuron systems with discrete delays. Chaos, Solitons & Fractals 21 (2004) 133-142
8. Cao J., and Xiao M. Stability and Hopf bifurcation in a simplified BAM neural network with two time delays. IEEE Trans Neural Networks 18 (2007) 416-430
9. Olien L., and Belair J. Bifurcation, stability and monotonicity properties of a delayed neural model. Physica D 102 (1997) 349-363
10. Wei J., and Ruan S. Stability and bifurcation in a neural network model with two delays. Physica D 130 (1999) 255-272
11. Guo S., Huang L., and Wang L. Linear stability and Hopf bifurcation in a two-neuron network with three delays. Int J Bifurcat Chaos 14 (2004) 2799-2810
12. Huang C., He Y., Huang L., and Z Y. Hopf bifurcation analysis of two neurons with three delays. Nonlinear Anal-Real 8 (2007) 903-921
13. Huang C., Huang L., Feng J., Nai M., and He Y. Hopf bifurcation analysis for a two-neuron network with four delays. Chaos, Solitons & Fractals 34 (2007) 795-812
14. Tank D.W., and Hopfield J.J. Neural computation by concentrating information in time. Proc Natl Acad Sci USA 84 (1987) 1896-1991
15. De Vries B., and Principle J.C. The gamma model - a new neural model for temporal processing. Neural Networks 5 (1992) 565-576
16. Principle J.C., Kuo J.-M., and Celebi S. An analysis of the gamma memory in dynamic neural networks. IEEE Trans Neural Networks 5 (1994) 337-361
17. Ruan S., and Filfil R.S. Dynamics of a two-neuron system with discrete and distributed delays. Physica D 191 (2004) 323-342
18. Liao X., Wong K.W., and Yang S. Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays. Phys Lett A 316 (2003) 55-64
19. Wang Z., Shu H., et al. Robust stability analysis of generalized neural networks with discrete and distributed time delays. Chaos, Solitons & Fractals 30 (2006) 886-896
20. Cao J., Yuan K., and Li H. Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans Neural Networks 17 (2006) 1646-1651
21. Park J.H. An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays. Chaos, Solitons & Fractals 32 (2007) 800-807
22. Song Y., and Yuan S. Bifurcation analysis in a predator-prey system with time delay. Nonlinear Anal 7 (2006) 265-284
23. Ruan S., and Wei J. 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) 863-874
24. Hassard B., Kazarinoff N., and Wan Y. Theory and application of Hopf bifurcation (1981), Cambridge University Press, Cambridge