Bursting and spiking due to additional direct and stochastic currents in neuron models
Yang Zhuo-Qin (杨卓琴)ab, Lu Qi-Shao (陆启韶)ab
a School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China; b Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing 100083, China
Abstract Neurons at rest can exhibit diverse firing activities patterns in response to various external deterministic and random stimuli, especially additional currents. In this paper, neuronal firing patterns from bursting to spiking, induced by additional direct and stochastic currents, are explored in rest states corresponding to two values of the parameter $V_{\rm K}$ in the Chay neuron system. Three cases are considered by numerical simulation and fast/slow dynamic analysis, in which only the direct current or the stochastic current exists, or the direct and stochastic currents coexist. Meanwhile, several important bursting patterns in neuronal experiments, such as the period-1 ``circle/homoclinic" bursting and the integer multiple ``fold/homoclinic" bursting with one spike per burst, as well as the transition from integer multiple bursting to period-1 ``circle/homoclinic" bursting and that from stochastic ``Hopf/homoclinic" bursting to ``Hopf/homoclinic" bursting, are investigated in detail.
Received: 22 October 2004
Revised: 06 September 2005
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10432010 and 10526002).
Cite this article:
Yang Zhuo-Qin (杨卓琴), Lu Qi-Shao (陆启韶) Bursting and spiking due to additional direct and stochastic currents in neuron models 2006 Chinese Physics 15 518
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