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Global stability and bifurcations of invariant measures for the discrete cocycles of the cardiac conduction system’s equations. (English) Zbl 1317.39008
Authors’ abstract: 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.

MSC:
39A12 Discrete version of topics in analysis
39A30 Stability theory for difference equations
39A10 Additive difference equations
34D23 Global stability of solutions to ordinary differential equations
37A20 Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations
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