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...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 VK 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 onc 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.展开更多
In this paper, we present a new idea to study the stochastic current within the canonical framework of white noise analysis. We define Wick-type stochastic current by using Wick integral with respect to Brownian motio...In this paper, we present a new idea to study the stochastic current within the canonical framework of white noise analysis. We define Wick-type stochastic current by using Wick integral with respect to Brownian motion, firstly. Moreover, we prove that the Brownian stochastic current is considered as a Hida distribution in terms of white noise approach and S-transform.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10432010 and 10526002）.Acknowledgement The bifurcation diagrams in this paper are obtained by means of the package C0NTENT.
文摘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 VK 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 onc 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.
基金Supported by National Natural Science Foundation of China(Grant No.11061032)Colleges and Universities Scientific Research Funds Project Plan of Gansu Province for Postgraduate Tutor(Grant No.1205-07)Colleges and Universities Fundamental Research Funds Project of Gansu Province(2012)
文摘In this paper, we present a new idea to study the stochastic current within the canonical framework of white noise analysis. We define Wick-type stochastic current by using Wick integral with respect to Brownian motion, firstly. Moreover, we prove that the Brownian stochastic current is considered as a Hida distribution in terms of white noise approach and S-transform.
