2011/03/17 by Martin Kell, Kell, Martin
Computer Science · Engineering · Physics and Astronomy · #37B35 #37L15 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Primary: 37B55 #Secondary: 37H99 #Stability and Controllability of Differential Equations #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1103.3458
openalex publication_date 2011/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using Conley theory we show that local attractors remain (past) attractors under small non-autonomous perturbations. In particular, the attractors of the perturbed systems will have positive invariant neighborhoods and converge upper semicontinuously to the original attractor. The result is split into a finite-dimensional part (locally compact) and an infinite-dimensional part (not necessarily locally compact). The finite-dimensional part will be applicable to bounded random noise, i.e. continuous time random dynamical systems on a locally compact metric space which are uniformly close the unperturbed deterministic system. The "closeness" will be defined via a (simpler version of) convergence coming from singular perturbations theory.