Codimension-two bifurcation analysis on firing activities in Chay neuron model

by: Lixia Duan, Qishao Lu

Chaos, Solitons & Fractals, Vol. 30, No. 5. (December 2006), pp. 1172-1179.

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Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.

@article{citeulike:759629, abstract = {Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.}, author = {Duan, Lixia and Lu, Qishao }, citeulike-article-id = {759629}, doi = {http://dx.doi.org/10.1016/j.chaos.2005.08.179}, journal = {Chaos, Solitons \& Fractals}, keywords = {neuron}, month = {December}, number = {5}, pages = {1172--1179}, posted-at = {2006-07-15 05:55:40}, priority = {2}, title = {Codimension-two bifurcation analysis on firing activities in Chay neuron model}, url = {http://dx.doi.org/10.1016/j.chaos.2005.08.179}, volume = {30}, year = {2006} }

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TY - JOUR ID - citeulike:759629 L3 - citeulike-article-id:759629 TI - Codimension-two bifurcation analysis on firing activities in Chay neuron model JF - Chaos, Solitons & Fractals VL - 30 IS - 5 SP - 1172 EP - 1179 N2 - Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing. KW - neuron AU - Duan, Lixia AU - Lu, Qishao PY - 2006/12// UR - http://dx.doi.org/10.1016/j.chaos.2005.08.179 ER -

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