Discrete-time map for an impulsive Goodwin oscillator with a distributed delay. Issue 1 (March 2016)

• Record Type: Journal Article
• Authors: Churilov, Alexander; Medvedev, Alexander
• Is Part Of: Mathematics of control, signals, and systems. Volume 28:Issue 1(2016)
• Page Start: 1
• Page End: 22
• Publication Date: 2016-03
• Subjects: Goodwin oscillator -- Impulsive equations -- Integro-differential equations; Control theory -- Periodicals; Signal processing -- Periodicals; System analysis -- Periodicals; 621.38223
• DOI: 10.1007/s00498-016-0160-y
• Languages: English
• ISSNs: 0932-4194

Abstract

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.