Based on actual neuronal firing activities, bursting in the Chay neuronal model is considered, in which VK, reversal potentials for K+, VC, reversal potentials for Ca2+, time kinetic constant λn and an additional dep...Based on actual neuronal firing activities, bursting in the Chay neuronal model is considered, in which VK, reversal potentials for K+, VC, reversal potentials for Ca2+, time kinetic constant λn and an additional depolarized current I are considered as dynamical parameters. According to the number of the Hopf bifurcation points on the upper branch of the bifurcation curve of fast subsystem, which is associated with the stable limit cycle corresponding to spiking states, different types of bursting and their respective dynamical behavior are surveyed by means of fast-slow dynamical bifurcation analysis.展开更多
The generic phantom bursting model proposed by Bertram et al.can evoke complex bursting oscillations in collaboration with two generic slow variables with different time scales.Two models with the phantom bursting mec...The generic phantom bursting model proposed by Bertram et al.can evoke complex bursting oscillations in collaboration with two generic slow variables with different time scales.Two models with the phantom bursting mechanism are suggested,when these two generic slow variables are provided with some specific biological significances by combining slowly varying intracellular Ca2+concentration of the Chay-Keizer electrical bursting model with two different glycolytic oscillations,respectively.Also,complex dynamic behaviors of different compound bursting occurring in these two models are comprehensively surveyed by two fast/slow analyses for a moderately and a slower slow variable,respectively.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10432010, 10526002 and 10702002)
文摘Based on actual neuronal firing activities, bursting in the Chay neuronal model is considered, in which VK, reversal potentials for K+, VC, reversal potentials for Ca2+, time kinetic constant λn and an additional depolarized current I are considered as dynamical parameters. According to the number of the Hopf bifurcation points on the upper branch of the bifurcation curve of fast subsystem, which is associated with the stable limit cycle corresponding to spiking states, different types of bursting and their respective dynamical behavior are surveyed by means of fast-slow dynamical bifurcation analysis.
基金supported by the National Natural Science Foundation of China(Grant Nos.1137201711072013 and 11202083)
文摘The generic phantom bursting model proposed by Bertram et al.can evoke complex bursting oscillations in collaboration with two generic slow variables with different time scales.Two models with the phantom bursting mechanism are suggested,when these two generic slow variables are provided with some specific biological significances by combining slowly varying intracellular Ca2+concentration of the Chay-Keizer electrical bursting model with two different glycolytic oscillations,respectively.Also,complex dynamic behaviors of different compound bursting occurring in these two models are comprehensively surveyed by two fast/slow analyses for a moderately and a slower slow variable,respectively.
