Bifurcation of burst response in an Amari-Hopfield neuron pair with a periodic external force

Electrical Engineering in Japan (English translation of Denki Gakkai Ronbunshi)

Volumn 146, Issue 2, 2004, Pages 43-53

  Tsuji, Shigeki ^a   Ueta, Tetsushi ^a   Kawakami, Hiroshi ^a   Aihara, Kazuyuki ^b  

^a UNIVERSITY OF TOKUSHIMA   (Japan)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

A periodic external force; Bifurcation; Burst response; Excitatory inhibitory neuron pair model

Indexed keywords

BIFURCATION (MATHEMATICS); ELECTROPHYSIOLOGY; MATHEMATICAL MODELS; NEURAL NETWORKS;

AMARI-HOPFIELD NEURON PAIR; BURST RESPONSE BIFURCATION; EXCITATORY-INHIBITORY NEURON PAIR MODEL;

ELECTRICAL ENGINEERING;

EID: 0346149975     PISSN: 04247760     EISSN: None     Source Type: Journal    
DOI: 10.1002/eej.10217     Document Type: Article

References (15)

1. Amari S. The mathematics of neural networks. Sangyo Publishing; 1978.
2. Aihara K. Chaos in Neural Systems. Tokyo Denki University Press; 1993.
3. Kawakami H (editor). Dynamic models and analysis of living rhythms. Corona Co.; 2001.
4. Kitajima H, Yoshinaga T, Aihara K, Kawakami H. Burst firing and bifurcation in chaotic neural networks with ring structure. Int J Bifurcation Chaos 2001;11:1631-1643.
5. Tsumoto K, Yoshinaga T, Kawakami H. Bifurcations in synaptically coupled BVP neurons. Int J Bifurcation Chaos 2001;11:1053-1064.
6. Hoppensteadt FC, Izhikevich EM. Weakly connected neural networks. Springer, ASM 126; 1997.
7. Izhikevich EM. Neural excitability, spiking and bursting. Int J Bifurcation Chaos 2000;10:1171-1266.
8. Rinzel J, Lee YS. Dissection of a model for neural parabolic bursting. J Math Biol 1987;25:653-675.
9. Bertram R, Butte MJ, Kiemel T, Sherman A. Topological and phenomenological classification of bursting oscillations. Bull Math Biol 1995;57:413-439.
10. Holden L, Erneux T. Slow passage through a Hopf bifurcation: From oscillatory to steady state solutions. SIAM J Appl Math 1993;53:1045-1058.
11. Holden L, Erneux T. Understanding bursting oscillations as periodic slow passage through bifurcation and limit points. J Math Biol 1993;31:351-365.
12. Smolen P, Terman D, Rinzel J. Properties of a bursting model with two slow inhibitory variables. SIAM J Appl Math 1993;53:861-892.
13. Pernarowski M. Fast subsystem bifurcations in a slowly varied Liénard system exhibiting bursting. SIAM J Appl Math 1994;54:814-832.
14. de Vries G. Multiple bifurcations in a polynomial model of bursting oscillations. J Nonlin Sci 1998;8:281-316.
15. Rush ME, Rinzel J. Analysis of bursting in a thalamic neuron model. Biol Cybern 1994;71:281-291.