Our research is focused on random dynamical systems generated by continuous self-mappings of an interval and their applications, for example, in population dynamics. We are interested in problems concerning complex behavior of these systems. Under certain conditions, the system stabilizes at some kind of equilibrium, hence its behavior is simple in some sense. Other systems may exhibit extremely unstable behavior which can be considered chaotic. For characterization of this complexity, we use notions of chaos known from the theory of discrete dynamical systems.

Selected papers

Janková K.: Chaos and stability in some random dynamical systems, Tatra Mt. Math. Publ. 51(1) (2012), 75-82.

Kováč J., Janková K.: Random Dynamical Dystems Generated by Two Allee Maps, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 27(8) (2017), 1750117.

Kováč J., Janková K.: Distributional chaos in random dynamical systems, J. Differ Equ. Appl. 25(4) (2019), 455–480.