Stability in the Whole and Bifurcations of Invariant Measures in Discrete-time Cocycles Generated by a Cardiac Conduction System
Author(s):
Anastasia A. Maltseva
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia
Postgraduate student
maltseva.anastacia@gmail.com
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.
vreitmann@aol.com
Abstract:
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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