Hybrid Integrate-and-Fire Model of a Bursting Neuron

Neural Computation

Volumn 15, Issue 12, 2003, Pages 2843-2862

  Breen, Barbara J ^a   Gerken, William C ^a   Butera Jr , Robert J ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ANIMAL; ARTICLE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; CELL MEMBRANE; CENTRAL NERVOUS SYSTEM; COMPARATIVE STUDY; COMPUTER SIMULATION; CYTOLOGY; HUMAN; NERVE CELL; NERVE CELL NETWORK; PHYSIOLOGY; REACTION TIME; RESPIRATION CENTER; SYNAPTIC TRANSMISSION;

ACTION POTENTIALS; ANIMALS; CELL MEMBRANE; CENTRAL NERVOUS SYSTEM; COMPUTER SIMULATION; HUMANS; MODELS, NEUROLOGICAL; NERVE NET; NEURAL NETWORKS (COMPUTER); NEURONS; REACTION TIME; RESPIRATORY CENTER; SYNAPTIC TRANSMISSION;

EID: 0242635707     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/089976603322518768     Document Type: Article

References (27)

1. Baer, S., Rinzel, J., & Carillo, H. (1995). Analysis of an autonomous phase model for neuronal parabolic bursting. Journal of Mathematical Biology, 33, 309-333.
2. Bertram, R. (1993). A computational study of the effects of serotonin on a mol-luscan burster neuron. Biological Cybernetics, 69, 257-267.
3. Bertram, R., Butte, M., Kiemel, T., & Sherman, A. (1995). Topological and phe-nomenological classification of bursting oscillations. Bulletin of Mathematical Biology, 57, 413-439.
4. Butera, R., Clark, J., & Byrne, J. (1996). Dissection and reduction of a modeled bursting neuron. Journal of Computational Neuroscience, 3, 199-223.
5. Butera, R. Clark, J., & Byrne, J. (1997). Transient responses of a modeled bursting neuron: Analysis with equilibrium and averaged nullclines. Biological Cybernetics, 77, 307-322.
6. Butera, R., Clark, J., Canavier, C., Baxter, D., & Byrne, J. (1995). Analysis of the effects of modulatory agents on a modeled bursting neuron: Dynamic interactions between voltage and calcium dependent systems. Journal of Computational Neuroscience, 2, 19-44.
7. Butera, R., Rinzel, J., & Smith, J. (1999a). Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons. Journal of Neurophysiology, 82, 382-397.
8. Butera, R., Rinzel, J., & Smith, J. (1999b). Models of respiratory rhythm generation in the pre-Bötzinger complex. II. Populations of coupled pacemakers. Journal of Neurophysiology, 82, 398-415.
9. Canavier, C., Clark, J., & Byrne, J. (1991). Simulation of the bursting activity of neuron R15 in Aplysia: Role of ionic currents, calcium balance, and modulatory transmitters. Journal of Neurophysiology, 66, 2107-2124.
10. Destexhe, A. (1997). Conductance-based integrate and fire models. Neural Computation, 9, 503-514.
11. Ermentrout, G. (1994). Reduction of conductance-based models with slow synapses to neural nets. Neural Computation, 6, 679-695.
12. Ermentrout, G. (2002). Simulating, analyzing, and animating dynamical systems: A guide to XPPAUT for researchers and students. Philadelphia: Society for Industrial and Applied Mathematics.
13. Hansel, D., & Mato, G. (2003). Asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons. Neural Computation, 15, 1-56.
14. Hines, M., & Carnevale, N. (1997). The NEURON simulation environment. Neural Computation, 9, 1179-1209.
15. Hines, M., & Carnevale, N. (2000). Expanding NEURON's repertoire of mechanisms with nmodl. Neural Computation, 12, 995-1007.
16. Izhikevich, E. (2000). Neural excitability, spiking, and bursting. International Journal of Bifurcation and Chaos, 10, 1171-1266.
17. Kepler, T., Abbott, L., & Marder, E. (1992). Reduction of conductance-based neuron models. Biological Cybernetics, 66, 381-387.
18. Koch, C. (1999). Biophysics of computation. New York: Oxford University Press.
19. Lapicque, L. (1907). Recherches quantitatives sur l'excitation électrique des nerfs traitée comme une polarization. Journal of Physiology (Paris), 9, 620-635.
20. MacGregor, R. J. (1987). Neural and brain modeling. San Diego, CA: Academic Press.
21. Press, W., Flannery, B., Teukolsky, S., & Vetterling, W. (1992). Numerical recipes in C (2nd ed.). Cambridge: Cambridge University Press.
22. Rinzel, J. (1985). Bursting oscillations in an excitable membrane model. In B. Sleeman & D. Jones (Eds.), Lecture notes in mathematics (Vol. 1151). Berlin: Springer-Verlag.
23. Rinzel, J. (1987). A formal classification of bursting mechanisms in excitable systems. In E. Teramoto & M. Yamaguti, (Eds.), Lecture notes in biomathematics (Vol. 71, pp. 267-281). Berlin: Springer-Verlag.
24. Rinzel, J., & Lee, Y. (1987). Dissection of a model for neuronal parabolic bursting. Journal of Mathematical Biology, 25, 653-675.
25. Smith, G., Cox, C., Sherman, S. M., & Rinzel, J. (2000). Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model. Journal of Neurophysiology, 83, 588-610.
26. Smolen, P., Terman, D., & Rinzel, J. (1993). Properties of a bursting model with two slow inhibitory variables. SIAM Journal of Applied Mathematics, 53, 861-892.
27. Terman, D. (1992). The transition from bursting to continuous spiking in excitable membrane models. Journal of Nonlinear Science, 2, 135-182.