Discrete-time modeling of a hereditary impulsive feedback system

The paper deals with a broad class of hybrid systems where a linear hereditary plant with a cascade structure operates under impulsive feedback. The plant incorporates a distinct infinite-dimensional block that might be a pointwise or distributed time delay. Mathematical models that belong to this class of systems appear in mathematical biology and computational medicine. A discrete time (Poincaré) map is constructed to capture the system dynamics and investigate its periodic solutions. Simulation results indicate that the effects on the system dynamics incurred by distributed delays are quite similar to those previously observed for pointwise delays. Generally, it appears that the complexity of the nonlinear dynamics does not increase with an increasing delay value.