Analysis of periodic solutions of a continuous dynamical system with delay and pumping

摘要

We analyze the existence of periodic solutions of a continuous dynamical system of special form with delay. The system has the specific feature that the unknown function changes in accordance with a delay differential equation until it reaches the zero value and then makes an instant jump to unity (pumping), after which it again satisfies the main differential equation until the next possible pumping. We find all periodic solutions of the original dynamical system with one pumping per period in the form of an exponential expansion. [PUBLICATION ABSTRACT]