Time delay induced multistability and complex dynamics in an impulsive model of endocrine regulation

The effects caused by the introduction of a time delay in the continuous part of an impulsive (hybrid) model of endocrine feedback regulation are studied by bifurcation analysis. It is concluded that larger (in some well-defined sense) values of the time delay give rise to a broad range of nonlinear dynamics phenomena that have not been observed for the smaller ones. Among such behaviors are e.g. border-collision bifurcations, bistability, and quasiperiodic solutions. The reason for the more complex dynamics exhibited by the model in this case is a discontinuity of the Jacobian of a discrete mapping describing the propagation of the model dynamics from one firing of the impulsive feedback to another.