Order-preserving random dynamical systems: Equilibria, attractors, applications. (English) Zbl 0938.37031

The extension of the notion of monotonicity for random dynamical systems (RDS), defined on a subset of a real Banach space with an order induced by a closed convex cone, is formulated. Several examples are provided. It is shown that every compact forward invariant set for a monotone RDS contains an equilibrium, and that an attractor of a monotone RDS is always contained in an interval given by two equilibria. Applications are discussed, among them a stochastic biochemical control circuit and random and stochastic parabolic equations.
Reviewer: H.Crauel (Berlin)


37H10 Generation, random and stochastic difference and differential equations
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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