A normal form for excitable vegetation dynamics

Abstract

[eng] In this work we study excitable dynamics related with vegetation ecosystems. In particular, we are interested in a model of Posidonia oceanica seagrass proposed by D. Ruiz-Reynes [1], which motivates the dynamical system studied in this project. This model introduces an autotoxicity mechanism, by means of sulfide production due to decomposition of the seagrass, which plays a negative feedback role in the dynamics. In this way, this model can display interesting and sophisticated phenomena such as spatio-temporal patterns. From a Dynamical Systems point of view, all these phenomena are related with a rich bifurcation diagram. Following the article of A. Arinyo-i Prats et. al. [2], we propose a simple dynamical system which presumably reproduces such bifurcation diagram. In particular, we pay attention on the excitable region appearing close to the Takens-Bugdanov point. We study the existence of excitable travelling pulses in this region when a diffusion term is added in the spatially extended model.