Discrete-time map for an impulsive Goodwin oscillator with a distributed delay. Issue 1 (March 2016) - Churilov, Alexander
Abstract A system of impulsive integro-differential equations representing a hybrid counterpart of the renown Goodwin oscillator is considered. The continuous part of the system possesses a cascade structure and contains a distributed bounded delay. The impulses impacting the continuous part are modulated in amplitude and frequency by the continuous output thus implementing an impulsive feedback. This kind of mathematical models appears in mathematical biology and computational medicine. Applying a version of the linear chain trick, it is demonstrated that a discrete-time (Poincaré) map can be constructed to capture the main dynamical properties of the system in hand.