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Bursting of Morris-Lecar neuronal model with current-feedback control

science china(Technological sciences) 2009年第3期52卷 771-781页

作者： duan lixia1, lu qishao2 & cheng daizhan3 1 college of science, north china university of technology, beijing 100144, china 2 School of science, beijing university of Aeronautics and Astronautics, beijing 100191, china 3 Institute of Systems science, Chinese Academy of sciences, beijing 100190, china college of science North China University of Technology Beijing China School of science Beijing University of Aeronautics and Astronautics Beijing China Institute of Systems science Chinese Academy of Sciences Beijing China

The Morris-Lecar (ML) neuronal model with current-feedback control is considered as a typical fast-slow dynamical system to study the combined influences of the reversal potential VCa of Ca2+ and the feedback current I on the generation and transition of different bursting oscillations. Two-parameter bifurcation analysis of the fast subsystem is performed in the parameter (I, VCa)-plane at first. Three important codimension-2 bifurcation points and some codimension-1 bifurcation curves are obtained which enable one to determine the parameter regions for different types of bursting. Next, we further divide the control parameter (V0, VCa)-plane into five different bursting regions, namely, the "fold/fold" bursting region R1, the "fold/Hopf" bursting region R2, the "fold/homoclinic" bursting region R3, the "subHopf/homoclinic" bursting region R4 and the "subHopf/subHopf" bursting region R5, as well as a silence region R6. Codimension-1 and -2 bifurcations are responsible for explanation of transition mechanisms between different types of bursting. The results are instructive for further understanding the dynamical behavior and mechanisms of complex firing activities and information processing in biological nervous systems.

关键词： neuron bursting bifurcation fast-slow dynamics analysis codimension

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Bursting of Morris-Lecar neuronal model with current-feedback control

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中国科学:技术科学 2010年第3期 346-346页

The Morris-Lecar (ML) neuronal model with current-feedback control is considered as a typical fast-slow dynamical system to study the combined influences of the reversal potential VCa of Ca2+ and the feedback current I on the generation and transition of different bursting ***-parameter bifurcation analysis of the fast subsystem is performed in the parameter (I,VCa)-plane at *** important codimension-2 bifurcation points and some codimension-1 bifurcation curves are obtained which enable one to determine the parameter regions for different types of ***,we further divide the control parameter (V0,VCa)-plane into five different bursting regions,namely,the "fold/fold" bursting region R1,the "fold/Hopf" bursting region R2,the "fold/homoclinic" bursting region R3,the "subHopf/homoclinic" bursting region R4 and the "subHopf/subHopf" bursting region R5,as well as a silence region ***-1 and-2 bifurcations are responsible for explanation of transition mechanisms between different types of *** results are instructive for further understanding the dynamical behavior and mechanisms of complex firing activities and information processing in biological nervous systems.

关键词： neuron bursting bifurcation fast-slow dynamics analysis codimension

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