title: Dynamical analysis of periodic bursting in piece-wise linear planar neuron model.
abstract: A piece-wise linear planar neuron model, namely, two-dimensional McKean model with periodic drive is investigated in this paper. Periodical bursting phenomenon can be observed in the numerical simulations. By assuming the formal solutions associated with different intervals of this non-autonomous system and introducing the generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the bursting solution induced by the slowly varying periodic drive is presented. It is shown that, the discontinuous Hopf bifurcation occurring at the non-smooth boundaries, i.e., the bifurcation taking place at the thresholds of the stimulation, leads the alternation between the rest state and spiking state. That is, different oscillation modes of this non-autonomous system convert periodically due to the non-smoothness of the vector field and the slow variation of the periodic drive as well.
authors.affiliation: Faculty of Science, Jiangsu University, Zhenjiang, 212013 China.
authors.forename: Ying
authors.initials: Y
authors.lastname: Ji
authors.affiliation: Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, 212013 China.
authors.forename: Xiaofang
authors.initials: X
authors.lastname: Zhang
authors.affiliation: Faculty of Science, Jiangsu University, Zhenjiang, 212013 China.
authors.forename: Minjie
authors.initials: M
authors.lastname: Liang
authors.affiliation: Faculty of Science, Jiangsu University, Zhenjiang, 212013 China.
authors.forename: Tingting
authors.initials: T
authors.lastname: Hua
authors.affiliation: Faculty of Science, Jiangsu University, Zhenjiang, 212013 China.
authors.forename: Yawei
authors.initials: Y
authors.lastname: Wang
keywords: Bursting; Generalized equilibrium state; Non-smooth bifurcation mechanism; Periodic drive; Piece-wise linear planar neuron model