Statistical solution and Liouville-type theorem for the nonautonomous discrete Selkov model

Abstract

In this article, we study the statistical solution of the nonautonomous discrete Selkov model. First, we show the existence of a pullback- attractor for the system and establish the existence of a unique family of invariant Borel probability measures carried by the pullback- attractor. Then we further prove that the family of invariant Borel probability measures is a statistical solution for the discrete system and satisfies a Liouville-type theorem. Finally, we demonstrate that the invariant property of the statistical solution is indeed a particular case of the Liouville-type theorem.