Selection mechanisms in front invasion

TL;DR

This paper reviews theoretical and practical aspects of front invasion into unstable states, emphasizing the role of invasion processes as selection mechanisms in complex systems.

Contribution

It highlights different perspectives and challenges in understanding front propagation, providing examples and computational guidance from a dynamical systems viewpoint.

Findings

Identifies open problems in front invasion theory

Discusses computational methods for studying invasion processes

Highlights invasion as a selection mechanism in complex systems

Abstract

We review progress on questions related to front propagation into unstable states and point out open problems in the area. We strive to highlight different theoretical perspectives and challenges while also addressing more practical questions with examples and guides to computational methods. Throughout we take a dynamical systems point of view that focuses on the ability of invasion processes to act as a selection mechanism in complex systems.