Reduction of a model for an Onchidium pacemaker neuron

Biological Cybernetics

Volumn 78, Issue 4, 1998, Pages 265-276

  Maeda, Yoshinobu ^a   Pakdaman, K ^a   Nomura, Taishin ^a   Doi, Shinji ^a   Sato, Shunsuke ^a  

^a OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOLOGICAL RHYTHM; COMPARATIVE STUDY; CYTOLOGY; ESOPHAGUS; GANGLION; INNERVATION; MOLLUSC; NERVE CELL; PHYSIOLOGY;

ANIMALS; BIOLOGICAL CLOCKS; ESOPHAGUS; GANGLIA, INVERTEBRATE; MODELS, NEUROLOGICAL; MOLLUSCA; NEURONS;

EID: 0032036715     PISSN: 03401200     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004220050432     Document Type: Article

References (24)

1. Abbott LF, Kepler TB (1990) Model neurons: from Hodgkin-Huxley to Hopfield. In: Garrido L (ed) Statistical mechanics of neural networks. Springer, Berlin Heidelberg New York, pp 5-18
2. Av-Ron E, Parnas H, Segel LA (1993) A basic biophysical model for bursting neurons. Biol Cybern 69:87-95
3. Bertram R, Butte MJ, Kiemel T, Sherman A (1995) Topological and phenomenological classification of bursting oscillations. Bull Math Biol 57:413-439
4. Chay TR (1985) Chaos in a three-variable model of an excitable cell. Physica D 16:233-242
5. Chay TR, Cook DL (1988) Endogenous bursting patterns in excitable cells. Math Biosci 90:139-153
6. Chay TR, Keizer J (1983) Minimal model for membrane oscillations in the pancreatic β-cell. Biophys J 42:181-190
7. Chay TR, Fan YS, Lee YS (1995) Bursting, spiking, chaos, fractals, and universality in biological rhythms. Int J Bifurcation Chaos 5:595-635
8. FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1:445-466
9. Golomb D, Guckenheimer J, Gueron S (1993) Reduction of a channel-based model for a stomatogastric ganglion LP neuron. Biol Cybern 69:129-137
10. Hayashi H, Ishizuka S (1992) Chaotic nature of bursting discharge in the Onchidium pacemaker neuron. J Theor Biol 156:269-291
11. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol (Lond) 117:504-544
12. Kepler TB, Abbott LF, Marder E (1992) Reduction of conductance-based neuron models. Biol Cybern 66:381-387
13. Matsumoto G (1981) Axonal excitability: its phenomena and molecular mechanism, vols 1 and 2. Maruzen (in Japanese)
14. Meunier C (1992) Two and three dimensional reductions of the Hodgkin-Huxley system: separation of time scales and bifurcation schemes. Biol Cybern 67:461-468
15. Nagumo J, Arimoto J, Yoshizawa S (1962) An active pulse transmission line stimulating nerve axon. Proc IRE 50:2061-2070
16. Noble D (1966) Applications of Hodgkin-Huxley equations to excitable tissues. Physiol Rev 46:1-50
17. ++ on bursting neurons. Biophys J 21:217-237
18. Plant RE (1981) Bifurcation and resonance in a model for bursting nerve cell. J Math Biol 11:15-32
19. Rinzel J (1985) Excitation dynamics: insights from simplified membrane models. Fed Proc 44:2944-2946
20. Rinzel J, Lee YS (1986) On different mechanisms for membrane potential bursting. In: Othmer HG (ed) Lecture notes in biomathematics, vol. 66. Springer, Berlin Heidelberg New York, pp 19-33
21. Rinzel J, Lee YS (1987) Dissection of a model for neuronal parabolic bursting. J Math Biol 25:653-675
22. Rose RM, Hindmarsh JL (1985) A model of a thalamic neuron. Proc R Soc Lond B 225:161-193
23. Rush ME, Rinzel J (1994) Analysis of bursting in a thalamic neuron model. Biol Cybern 71:281-291
24. Sherman A, Rinzel J, Keizer J (1988) Emergence of organized bursting in clusters of pancreatic β-cells by channel sharing. Biophys J 54:411-425