Ultradian Rhythmicity and Chaotic Behaviors in the Integrate-and-Fire Model of a Neuroendocrine System

Abstract

We consider a mathematical model for pulsatility in a neuroendocrine regulation system. The impulsive neural activity is modeled using an integrate-and-fire mechanism, applied to ensembles of hypothalamic neurons. The system generates a discrete impulse-to-impulse mapping that can be used to detect periodic and chaotic behaviors. The numerical study of this mapping is illustrated with bifurcation diagrams. In a wide range of the model’s parameters, transition to chaos through cascades of period-doubling bifurcations was found. Merging and expansion bifurcations were also revealed in the system.