Dynamics Analysis of Neuron Bursting under the Modulation of Periodic Stimulation

A nonsmooth neuron model with periodic excitation which can reproduce spiking and bursting behavior of cortical neurons is investigated in this paper. Based on nonsmooth bifurcation analysis, the mechanism of the bursting behavior induced by slow-changing periodical stimulation as well as the associated evolution with the variation of the stimulation is explored. The modulating character of the external excitation and the effect of the bifurcation occurring at the switching boundary of the vector field are presented.

UNFOLDING NONSMOOTH BIFURCATION PATTERNS IN A 1-D PWL MAP AS A MODEL OF A SINGLE-INDUCTOR TWO-OUTPUT DC–DC SWITCHING CONVERTER

A piecewise linear (PWL) continuous map is used to analyze the nonsmooth bifurcation phenomena in a single-inductor two-output (SITO) DC–DC converter under a PWM interleaved control scheme. This map models the dynamical behavior of the converter when the waveforms of the inductor current can be approximated by straight lines during each switching subinterval. The parameter space is constrained by the interleaving control and the physical restriction on the values of some parameters. The main focus of this paper is on the existence and stability conditions of the rich variety of k-periodic orbits and the different bifurcation patterns that can be exhibited in this system. The analytical results in the form of 1-D and 2-D bifurcation diagrams are compared with numerical simulations obtained from the circuit-based switched model getting a good agreement between the two approaches.