Multistability and hidden attractors in an impulsive Goodwin oscillator with time delay

The release of luteinizing hormone (LH) is driven by intermittent bursts of activity in the hypothalamic nerve centers of the brain. Luteinizing hormone again stimulates release of the male sex hormone testosterone (Te) and, via the circulating concentration of Te, the hypothalamic nerve centers are subject to a negative feedback regulation that is capable of modifying the intermittent bursts into more regular pulse trains. Bifurcation analysis of a hybrid model that attempts to integrate the intermittent bursting activity with a continuous hormone secretion has recently demonstrated a number of interesting nonlinear dynamic phenomena, including bistability and deterministic chaos. The present paper focuses on the additional complexity that arises when the time delay in the continuous part of the model exceeds the typical bursting interval of the feedback. Under these conditions, the hybrid model is capable of displaying quasiperiodicity and border collisions as well as multistability and hidden attractors.