ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Stability in the Whole and Bifurcations of Invariant Measures in Discrete-time Cocycles Generated by a Cardiac Conduction System


Anastasia A. Maltseva

Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia
Postgraduate student

Volker Reitmann

70 corp.3, Botanicheskaya st,
Peterhof, Saint-Petersburg,
198516, Russia
Saint-Petersburg State University
professor of the Department of Applied Cybernetics
Prof. Dr.


In this paper parameter-dependent cocycles generated by nonautonomous difference equations are considered. As an example of equations of this type a discrete-time cardiac conduction model is investigated. For this system with a control variable a cocycle is constructed. The theorem about global stability of discrete-time cocycles is stated. The existence of an invariant measure for such a cocycle is investigated using some elements of the Perron-Frobenius operator theory, and bifurcations of parameter-dependent measures are discussed.


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