Global stability and bifurcations of invariant measures for the discrete cocycles of the cardiac conduction system’s equations

In the present paper, we study parameter-depending cocycles generated by nonautonomous difference equations. The time-discrete model of the cardiac conduction system is an example of such equations. We construct a cocycle for such a system with a control variable. We present a theorem on the global...

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Bibliographic Details
Published in:Differential equations 2014-12, Vol.50 (13), p.1718-1732
Main Authors: Maltseva, A. A., Reitmann, V.
Format: Article
Language:English
Subjects:
Bifurcations
Control systems
Difference and Functional Equations
Difference equations
Differential equations
Dynamical Systems
Invariants
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Operators
Ordinary Differential Equations
Partial Differential Equations
Stability
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Summary:In the present paper, we study parameter-depending cocycles generated by nonautonomous difference equations. The time-discrete model of the cardiac conduction system is an example of such equations. We construct a cocycle for such a system with a control variable. We present a theorem on the global stability for time-discrete cocycles. We also study the existence of an invariant measure for such a cocycle by using some elements of the Perron-Frobenius operators’ theory and discuss bifurcations of parameter-dependent measures.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266114130035