Coexistence of tonic spiking oscillations in a leech neuron model

被引:60
作者
Cymbalyuk, G [1 ]
Shilnikov, A
机构
[1] Georgia State Univ, Dept Phys & Astron, Atlanta, GA 30303 USA
[2] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA
关键词
Pontryagin's averaging method; chaos; chaotic tonic spiking; bi-stability; bifurcation; transition; period-doubling;
D O I
10.1007/s10827-005-0354-7
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
The leech neuron model studied here has a remarkable dynamical plasticity. It exhibits a wide range of activities including various types of tonic spiking and bursting. In this study we apply methods of the qualitative theory of dynamical systems and the bifurcation theory to analyze the dynamics of the leech neuron model with emphasis on tonic spiking regimes. We show that the model can demonstrate bi-stability, such that two modes of tonic spiking coexist. Under a certain parameter regime, both tonic spiking modes are represented by the periodic attractors. As a bifurcation parameter is varied, one of the attractors becomes chaotic through a cascade of period-doubling bifurcations, while the other remains periodic. Thus, the system can demonstrate co-existence of a periodic tonic spiking with either periodic or chaotic tonic spiking. Pontryagin's averaging technique is used to locate the periodic orbits in the phase space.
引用
收藏
页码:255 / 263
页数:9
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