It is a fundamental challenge to understand how the function of a network is related to its
structural organization. Adaptive dynamical networks represent a broad class of systems that …

Currently the number of reduction methods used in practice in climate applications is vast
and tends to be difficult to access for researchers searching for an overview of the area. In …

We present a rigorous analysis of the slow passage through a Turing bifurcation in the Swift-
Hohenberg equation using a novel approach based on geometric blow-up. We show that …

We study a singularly perturbed fast-slow system of two partial differential equations (PDEs)
of reaction-diffusion type on a bounded domain. We assume that the reaction terms in the …

We consider a fast-slow partial differential equation (PDE) with reaction-diffusion dynamics
in the fast variable and the slow variable driven by a differential operator on a bounded …

We extend classical finite-dimensional Fenichel theory in two directions to infinite
dimensions. Under comparably weak assumptions we show that the solution of an infinite …

We study a singularly perturbed fast-slow system of two partial differential equations (PDEs)
of reaction-diffusion type on a bounded domain via Galerkin discretisation. We assume that …

The aim of this expository paper is twofold. We start with a concise overview of the theory of
invariant slow manifolds for fast-slow dynamical systems starting with the work by Tikhonov …

In this paper we generalize the Fenichel theory for attracting critical/slow manifolds to fast-
reaction systems in infinite dimensions. In particular, we generalize the theory of invariant …

Geometric singular perturbation theory (GSPT) has proven to be an invaluable tool for the
study of multiple time scale ordinary differential equations (ODEs). The extension of the …