Bautin bifurcation analysis for synchronous solution of a coupled FHN neural system with delay

Communications in Nonlinear Science and Numerical Simulation

Volumn 15, Issue 2, 2010, Pages 442-458

  Zhen, Bin ^a   Xu, Jian ^a  

^a TONGJI UNIVERSITY   (China)

Author keywords

02.30.Oz; 05.45. a; Bautin bifurcation; Coupled FHN neural system; Nonlinear dynamics; Time delay

Indexed keywords

DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; TIME DELAY;

-A; 02.30.; 05.45.; BAUTIN BIFURCATION; CONDITION; COUPLED FHN NEURAL SYSTEM; NEURAL SYSTEMS; OZ; SYSTEMS WITH DELAYS; TIME-DELAYS;

BIFURCATION (MATHEMATICS);

EID: 69049107414     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.04.006     Document Type: Article

References (20)

1. FitzHugh R. Impulses and physillogical states in theoretical models of nerve membrane. Biophys J 1 (1961) 445-466
2. Nagumo J., Arimoto S., and Yoshizawa S. An active pulse transmission line simulating nerve axon. Proc IRE 50 (1962) 2061-2070
3. Shepherd G.M. Neurobiology (1983), Oxford University, New York
4. Murray J.D. Mathematical biology (1990), Springer, New York
5. Tetsushi U., Hisayo M., Takuji K., and Hiroshi K. Bifurcation and chaos in coupled BVP oscillators. Int J Bifur Chaos 4 14 (2004) 1305-1324
6. Tetsushi U., and Hiroshi K. Bifurcation in asymmetrically coupled BVP oscillators. Int J Bifur Chaos 5 13 (2003) 1319-1327
7. Kunichika T., Kazuyuki A., and Hiroshi K. Bifurcations in synaptically coupled BVP nerons. Int J Bifur Chaos 4 11 (2001) 1053-1064
8. Nikola B., and Dragana T. Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling. Phys Rev E 67 (2003) 0662215-0662221
9. Nikola B., Ines G., and Nebojsa V. Type I vs. type II excitable systems with delayed coupling. Chaos, Solitons & Fractals 23 2 (2005) 1221-1233
10. Wang Q., Lu Q., and Chen G. Bifurcation and synchronization of synaptically coupled FHN models with time delay. Chaos, Solitons & Fractals 39 (2009) 918-925
11. Ion A-V. On the Bautin bifurcation for systems of delay differential equations. In: Proceedings of ICTAMI 2004. vol. 8, Thessaloniki, Breece: Acta Univ. Apulensis; 2004. p. 235-46.
12. Ion A.-V. An example of Bautin-type bifurcation in a delay differential equation. J Math Anal Appl 329 (2007) 777-789
13. Hale J. Theory of functional differential equations (1977), Springer, New York
14. Kuznetsov Y. Elements of applied bifurcation theory. Appl Math Sci Vol. 112 (1995), Springer, New York
15. Drover J.D., and Ermentrout B. Nonlinear coupling near a degenerate Hopf (Bautin) bifurcation. SIAM J Appl Math 63 (2003) 1627-1647
16. Govaerts W., and Sautois W.B. Computation of the phase response curve: a direct numerical approach. Neural Comput 18 (2006) 817-847
17. Govaerts W., Kuznetsov Y.A., and Sijnave B. Numerical methods for the generalized Hopf bifurcation. SIAM J Numer Anal 38 (2000) 329-346
18. Yang X., Yang M., Liu H., and Liao X. Bautin bifurcation in a class of two-neuron networks with resonant bilinear terms. Chaos, Solitons & Fractals 38 (2008) 575-589
19. Burić N., and Todorović D. Bifurcations due to small time-lag in coupled excitable systems. Int J Bifur Chaos 15 (2005) 1775-1785
20. Drover J.D., and Ermentrout B. Nonlinear coupled near a degenerate Hopf (Bautin) bifurcatio. SIAM J Appl Math 63 5 (2003) 1627-1647