Dondl, Patrick W. ; Scheutzow, Michael ; Throm, Sebastian (2015)
For a model of a driven interface in an elastic medium with random obstacles we prove the existence of a stationary positive supersolution at non-vanishing driving force. This shows the emergence of a rate-independent hysteresis through the interaction of the interface with the obstacles despite a linear (force = velocity) microscopic kinetic relation. We also prove a percolation result, namely...On the random dynamics of Volterra quadratic operators
Jamilov, U. U. ; Scheutzow, M. ; Wilke-Berenguer, M. (2015)
We consider random dynamical systems generated by a special class of Volterra quadratic stochastic operators on the simplex Sm-1. We prove that in contrast to the deterministic set-up the trajectories of the random dynamical system almost surely converge to one of the vertices of the simplex Sm-1, implying the survival of only one species. We also show that the minimal random point attractor o...