A mechanism for elliptic-like bursting and synchronization of bursts in a map-based neuron network

Cognitive Processing

Volumn 10, Issue 1 SUPPL., 2009, Pages 23-31

  Cao, Hongjun ^a,b   Sanjuán, Miguel A F ^b  

^a BEIJING JIAOTONG UNIVERSITY   (China)

^b UNIVERSIDAD REY JUAN CARLOS   (Spain)

Author keywords

Bursting; Map neurons; Synchronization

Indexed keywords

ARTICLE; CELL SYNCHRONIZATION; ELECTRIC ACTIVITY; NERVE CELL NETWORK; NEUROTRANSMISSION; OSCILLATION; PRIORITY JOURNAL;

ACTION POTENTIALS; ANIMALS; ELECTROPHYSIOLOGY; EXCITATORY POSTSYNAPTIC POTENTIALS; MODELS, NEUROLOGICAL; NERVE NET; NEURAL INHIBITION; NEURONS; NONLINEAR DYNAMICS; SYNAPSES;

EID: 60549110420     PISSN: 16124782     EISSN: 16124790     Source Type: Journal    
DOI: 10.1007/s10339-008-0222-2     Document Type: Article

References (20)

1. J Best A Borisyuk J Rubin D Terman M Wechselberger 2005 The dynamic range of bursting in a model respiratory pacemaker network SIAM J Appl Dyn Syst 4 1107 1139
2. Cao HJ, Ibarz B, Tanaka G, Sanjuán MAF (2007) The effect of asymmetry on generation and synchronization of bursts. Phys Rev E (submitted)
3. JM Casado 2003 Transient activation in a network of coupled map neurons Phys Rev lett 91 20
4. JM Casado B Ibarz MAF Sanjuan 2004 Winnerless competition in networks of coupled neurons Modern Phys Lett B 18 1347
5. DR Chialvo 1995 Generic excitable dynamics on a two-dimensional map Chaos Solitons Fractals 5 461
6. G de Vries 2001 Bursting as an emergent phenomenon in coupled chaotic maps Phys Rev E 64 051914 1
7. RC Elson AI Selverston R Huerta NF Rulkov MI Rabinovich HDI Abarbanel 1998 Synchronous Behavior of Two Coupled Biological Neurons Phys Rev Lett 81 5692
8. Gerstner W, Kistler WM (1999) Spiking neuron models. Cambridge University press, Cambridge
9. B Ibarz G Tanaka MAF Sanjuán K Aihara 2007 Sensitivity versus resonance in two-dimensional spiking-bursting neuron models Phys Rev E 75 041902
10. Ibarz B, Cao HJ, Sanjuán MAF (2007b) Map-based neuron networks. In: Garrido PL, Marro J (eds) 9th Granada Seminar on computational and statistical physics, AIP Proceedings, 887. Melville, New York, p 69
11. B Ibarz JM Casado MAF Sanjuán 2007 Patterns in inhibitory networks of simple map neurons Phys Rev E 75 041911
12. EM Izhikevich 2000 Neural excitability, spiking and bursting Int J Bifurcat Chaos 10 1171
13. Izhikevich EM (2007) Dynamical systems in neuroscience: the geometry of excitability and bursting. The MIT press, Cambridge
14. H Nozawa 1992 A neural network model as a globally coupled map and applications based on chaos Chaos 2 377
15. Rinzel J (1987) Mathematical topics in population biology, morphogenesis, and neuroscience. Springer, New York
16. NF Rulkov 2001 Regularization of synchronized chaotic bursts Phys Rev Lett 86 183
17. NF Rulkov I Timofeev M Bazhenov 2004 Oscillations in large-scale cortical networks: map-based model J Comput Neurosci 17 203
18. AL Shilnikov NF Rulkov 2004 Subthreshold oscillations in a map-based neuron model Phys Lett A 328 177
19. G Tanaka B Ibarz MAF Sanjuán K Aihara 2006 Synchronization and propagation of bursts in a ring of coupled map neurons Chaos 16 013113
20. A Sherman 1996 Contributions of modeling to understanding stimulus secretion coupling in pancreatic β-cells Am J Physiol Endocrinol Metab 271 E362 E372