Anastasia Maltseva, Volker Reitmann, Saint Petersburg State University, Department of Mathematics and Mechanics, 198504, Universitetsky prospekt 28, Peterhof, Saint Petersburg, Russia, e-mail: maltseva.anastacia@gmail.com, vreitmann@aol.com
Abstract: We consider parameter-dependent cocycles generated by nonautonomous difference equations. One of them is a discrete-time cardiac conduction model. For this system with a control variable a cocycle formulation is presented. We state a theorem about upper Hausdorff dimension estimates for cocycle attractors which includes some regulating function. We also consider the existence of invariant measures for cocycle systems using some elements of Perron-Frobenius theory and discuss the bifurcation of parameter-dependent measures.
Keywords: discrete-time parameter-dependent cocycles; Hausdorff dimension estimate; invariant measure
Classification (MSC 2010): 35B15, 35K20
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