中国物理B ›› 2006, Vol. 15 ›› Issue (3): 518-525.doi: 10.1088/1009-1963/15/3/012

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Bursting and spiking due to additional direct and stochastic currents in neuron models

杨卓琴, 陆启韶   

  1. School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China; Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing 100083, China
  • 收稿日期:2004-10-22 修回日期:2005-09-06 出版日期:2006-03-20 发布日期:2006-03-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10432010 and 10526002).

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   

  1. 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
  • Received:2004-10-22 Revised:2005-09-06 Online:2006-03-20 Published:2006-03-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10432010 and 10526002).

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摘要： 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.

关键词: direct current, stochastic current, bursting and spiking, fast/slow dynamic analysis

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.

Key words: direct current, stochastic current, bursting and spiking, fast/slow dynamic analysis

中图分类号:  (General theory and mathematical aspects)

  • 87.10.-e
87.19.L- (Neuroscience) 05.45.-a (Nonlinear dynamics and chaos)