Stability and bifurcation in a simplified five-neuron BAM neural network with delays

Chaos, Solitons and Fractals

Volumn 42, Issue 4, 2009, Pages 2357-2363

  Yang, Yu ^a   Ye, Jin ^b  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b DONGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ASSOCIATIVE PROCESSING; HOPF BIFURCATION;

BAM NEURAL NETWORK; BI-DIRECTIONAL ASSOCIATIVE MEMORY; CRITICAL VALUE; STABILITY AND BIFURCATION;

NEURAL NETWORKS;

EID: 67650998706     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2009.03.123     Document Type: Article

References (31)

1. Cao J.D. On stability analysis in delayed celler neural networks. Phys Rev E 59 (1999) 5940-5944
2. Cao J.D. Periodic oscillation solution of bidirectional associative memory networks with delays. Phys Rev E 59 (2000) 1825-1828
3. Chen A.P., Cao J.D., and Huang L.H. Exponential stability of BAM neural networks with transmission delays. Neurocomputing 57 (2004) 435-454
4. Chen A.P., Huang L.H., and Cao J.D. Existence and stability of almost periodic solution for BAM neural networks with delays. Appl Math Comput 137 (2003) 177-193
5. Fan D.J., and Wei J.J. Hopf bifurcation analysis in a tri-neuron network with time delay. Nonlinear Anal Real World Appl 9 (2008) 9-25
6. Gopalsamy K., and He X.Z. Delay-independent stability in bidirectional associative memory networks. IEEE Trans Neural Networks 5 (1994) 998-1002
7. Huang C.X., Huang L.H., Feng J.F., Nai M.Y., and He Y.G. Hopf bifurcation analysis for a two-neuron network with four delays. Chaos, Solitons & Fractals 34 (2007) 795-812
8. Huang X., Cao J.D., and Huang D.S. LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks. Chaos, Solitons & Fractals 34 (2007) 795-812
9. Liao X.X. Stability of the Hopfield neural networks. Sci China 23 (1993) 523-532
10. Li X.L., and Wei J.J. On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays. Chaos, Solitons & Fractals 26 (2005) 519-526
11. Li Y.K. Global exponential stability of BAM neural networks with delays and impulses. Chaos, Solitons & Fractals 24 (2005) 279-285
12. Mohamad S. Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks. Physica D 159 (2001) 233-251
13. Park J.H. A novel criterion for global asymptotic stability of BAM neural networks with time delays. Chaos, Solitons & Fractals 29 (2006) 446-453
14. Ruan S.G., and Wei J.J. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynam Cont Dis 10 (2003) 863-874
15. Song Y.L., Han M.A., and Wei J.J. Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays. Physica D 200 (2005) 185-204
16. Wang H., Liao X.F., and Li C.D. Existence and exponential stability of periodic solution of BAM neural networks with impulse and time-varying delay. Chaos, Solitons & Fractals 33 (2007) 1028-1039
17. Wang L., and Zou X.F. Hopf bifurcation in bidirectional associative memory neural networks with delays: analysis and computation. J Comput Appl Math 167 (2004) 73-90
18. Wang Z.D., Liu Y.R., and Liu X.H. On global asymptotic stability of neural networks with discrete and distributed delays. Phys Lett A 345 (2005) 299-308
19. Wei J.J., and Zhang C.R. Bifurcation analysis of a class of neural networks with delays. Nonlinear Anal Real World Appl 9 (2008) 2234-2252
20. Wu J.H. Introduction to neural dynamics and signal transmission delay (2001), Walter de Cruyter, Berlin
21. Yan X.P. Hopf bifurcation and stability for a delayed tri-neuron network model. J Comput Appl Math 196 (2006) 579-595
22. Yan X.P., and Li W.T. Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays. Dis Dyn Nat Soc (2006) 1-29
23. Yang X.F., Yang M.B., Liu H.Y., and Liao X.F. Bautin bifurcation in a class of two-neuron networks with resonant bilinear terms. Chaos, Solitons & Fractals 38 (2008) 575-589
24. Yu W.W., and Cao J.D. Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays. Phys Lett A 351 (2006) 64-78
25. Zhang C.R., and Zheng B.D. Hopf bifurcation in numerical approximation of a n-dimension neural network model with multi-delays. Chaos, Solitons & Fractals 25 (2005) 129-146
26. Zhang C.R., and Zheng B.D. Stability and bifurcation of a two-dimension discrete neural network model with multi-delays. Chaos, Solitons & Fractals 31 (2007) 1232-1242
27. Zhang C.R., Zheng B.D., and Wang L.C. Multiple Hopf bifurcations of symmetric BAM neural network model with delay. Appl Math Lett 22 (2009) 616-622
28. Zhang T.L., Jiang H.J., and Teng Z.D. On the distribution of the roots of a fifth degree exponential polynomial with application to a delayed neural network model. Neurocomputing 72 (2009) 1098-1104
29. Zhao H.Y. Global stability of bidirectional associative memory neural networks with distributed delays. Phys Lett A 297 (2002) 82-190
30. Zheng B.D., Zhang Y.Z., and Zhang C.R. Global existence of periodic solutions on a simplified BAM neural network model with delays. Chaos, Solitons & Fractals 37 (2008) 1397-1408
31. Zheng B.D., Zhang Y., and Zhang C.R. Stability and bifurcation of a discrete BAM neural network model with delays. Chaos, Solitons & Fractals 36 (2008) 612-616