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Bifurcations of invariant measures in discrete-time parameter dependent cocycles. (English) Zbl 1349.35042
Summary: 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.

MSC:
35B41 Attractors
35B15 Almost and pseudo-almost periodic solutions to PDEs
35B32 Bifurcations in context of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
37H05 General theory of random and stochastic dynamical systems
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