Bifurcating Neurones

Holden, Arun V.; Hyde, James; Muhamad, Mudiana; Zhang, H. G.

doi:10.1007/978-1-4471-1965-4_3

Cited by 1 publication

(2 citation statements)

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“…Having analyzed the models describing ionic mechanisms of the neuron membrane oscillations (Plant 1981;Chay 1985;Chay and Rinzel 1985;Rinzel and Lee 1987;Holden et al 1992;) based on the Hodgkin±Huxley formalism (Hodgkin and Huxley 1952), we chose dierential equations, to which all the models can be reduced. The system has the form…”

Section: The Modelmentioning

confidence: 99%

“…Bursting oscillations in excitable membrane models have been studied over the past decade (Hindmarsh and Rose 1984;Degn et al 1987;Terman 1991;Holden et al 1992) to explain the mechanism of burst generation. The works provide pictorial renditions of (1) the boundary in the model parameter space as the electrical activity of the membrane qualitatively changes (from periodic spikes to bursts); (2) the dependence of the burst mode (number of spikes/burst) on the model parameters.…”

Section: Introductionmentioning

confidence: 99%

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Method for constructing the boundary of the bursting oscillations region in the neuron model

Bedrov

Dick

Nozdrachev

et al. 2000

Biological Cybernetics

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We examine the problem of constructing the boundary of bursting oscillations on a parameter plane for the system of equations describing the electrical behaviour of the membrane neuron arising from the interaction of fast oscillations of the cytoplasma membrane potential and slow oscillations of the intracellular calcium concentration. As the boundary point on the parameter plane we consider the values at which the limit cycle of the slow subsystem is tangent to the Hopf bifurcation curve of the fast subsystem. The method suggested for determining the boundary is based on the dissection of the system variables into slow and fast. The strong point of the method is that it requires the integration of the slow subsystem only. An example of the application of the method for the stomatogastric neuron model [Guckenheimer J, Gueron S, Harris-Warrick RM (1993) Philos Trans R Soc Lond B 341: 345-359] is given.

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