K-dimensional invariant cones of random dynamical systems in Rn with applications

We investigated a linear random dynamical system which strongly preserves a cone C of dimension-k (abbr. k-cone) in R-n. Under some general assumptions, it is shown that such system admits a measurable family of k-dimensional subspaces and a measurable family of (n - k)-dimensional subspaces which are complementary to each other and form into a tempered invariant splitting of R-n. We further apply the measurable bundles so obtained to study the linear random monotone cyclic feedback systems, as well as the linear competitive-cooperative tridiagonal systems. This generalizes the Floquet theory for these deterministic non-autonomous (or time-periodic) systems to the random systems. (C) 2015 Elsevier Inc. All rights reserved.