Bursting and spiking due to additional direct and stochastic currents in neuron models |
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Authors: | Yang Zhuo-Qin and Lu Qi-Shao |
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Institution: | 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 |
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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. |
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Keywords: | direct current stochastic current bursting and spiking fast/slow dynamic
analysis |
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