The research for Hopf bifurcation in a single inertial neuron model with external forcing

Proceedings - 2007 IEEE International Conference on Granular Computing, GrC 2007

Volumn , Issue , 2007, Pages 528-533

  Liu, Qun ^a,b   Liao, Xiaofeng ^a   Yang, Degang ^a   Guo, Songtao ^a  

^a CHONGQING UNIVERSITY   (China)

^b CHONGQING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CENTER MANIFOLD; CLOSED FORM; DELAYED DIFFERENTIAL EQUATIONS; EXTERNAL FORCING; GRANULAR COMPUTING (GRC); INTERNATIONAL CONFERENCES; NEURON MODELS; PERIODIC SOLUTIONS; SINGLE NEURON;

BESSEL FUNCTIONS; BIFURCATION (MATHEMATICS); DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS);

HOPF BIFURCATION;

EID: 46749089656     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/GRC.2007.4403155     Document Type: Conference Paper

References (14)

1. X.F. Liao, G.R. Chen, "Local stability, Hopf an resonant codimension-two bifurcation in a harmonic oscillator with two time delays", Int.J.Bifurc.Chaos, 11(2001), pp. 2105-2121
2. X.F. Liao, G.R. Chen, "Hopf bifurcation and chaos analysis of Chen's system with distributed delays", Chaos, Soliton Fractals, 25(2005) pp. 197-220.
3. W.W. Yu, J.D. Cao, "Hof bifurcation and stability of periodic solutions for van der Pol equation with time delay", Nonliear Analyis, 62(2005), pp. 141-165.
4. X.F. Liao, J.B. Yu, "Robust stability for interval Hopfield neural networks with time delay", IEEE Trans, NN9(5)(1998), pp. 1042-1046.
5. X.F. Liao, Z.F. Wu, J.B. Yu, "Stability switches, bifurcations and stability of periodic solutions for neural network with continuous time delay", IEEE Trans, Syst.Man Cybern, Part A 29(1999), 692-696
6. C.G. Li, G.R. Chen, X.F. Liao, J.B. Yu, "Hopf bifurcation and chaos in a single inertial neuron model with time delay", Eur.Phys.J.B, 41(2004), pp. 337-343
7. B.D. Hassard, N.D. Kazarinoff N.D., Y.H. Wan, "Theory and applications of Hof bifurcation", Cambridge:Cambridge University Press, 1981
8. A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations, Wiley, New York, 1979
9. D.W. Wheeler, W.C. Schieve, "Stability and chaos in an inertial two-neuron system", Physica D, 105(1997), pp. 267-284
10. J. Xu, K.W. Chung, "Effects of time delayed position feedback on a van der Pol-Dyffing oscillator", Physica D, 180(2003), pp. 17-39
11. J.C.Ji, C.H. Hansen, X.Y. Li, "Effect of external excitations on a nonlinear system with time delay", Nonlinear Cynamics, 41(2005), pp. 385-402
12. J. Xu, Q.S. Lu, "Bifurcations and chaos due to time delay in a delayed control non-autonomous system", Acta Mechanica Sinica, 35(2003), pp. 443-451 (In Chinese)
13. H.S.Y. Chan, K.W. Chung, D.W. Qi, "Some bifurcation diagrams for limit cycles of quadratic differential systems", Int.J.Bifurc.Chaos, 11(2001), pp. 197-206
14. X.F. Liao, Q.Liu, W. Zhang, "Delayed-dependent asymptotic stability for neural networks with distributed delays", Nonlinear Analysis: Real world applications, 7(2006), pp. 1178-1192