This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

Approximate aggregation techniques allow one to transform a complex system involving
many coupled variables into a simpler reduced model with a lesser number of global …

In this paper, we provide a brief review of the well-known methods of reducing spatially
structured population models to mean-field models. First, we discuss the terminology of …

We formulate and analyze an archetypal consumer–resource model in terms of ordinary
differential equations that consistently translates individual life history processes, in …

Ecological modelers produce models with more and more details, leading to dynamical
systems involving lots of variables. This chapter presents a set of methods which aim to …

In this paper, we study a mathematical bio-economic model of a fishery with varying price.
The three dimensional model describes the time evolution of the resource, the fishing effort …

In this work, we study a model of the chemostat where the species are present in two forms,
isolated and aggregated individuals, such as attached bacteria or bacteria in flocks. We …

Modelling ecological systems implies to take into account different ecological levels: the
individual, population, community and ecosystem levels. Two large families of models can …

Organized complexity is a characteristic feature of ecological systems with heterogeneous
components interacting at several spatio-temporal scales. The hierarchy theory is a powerful …

In ecology, we are faced with modelling complex systems involving many variables
corresponding to interacting populations structured in different compartmental classes, ages …