Description du sujet de thèse

This PhD project aims to achieve both theoretical advances and practical applications. It will focus on the study of predator-prey models involving interactions between otters, crayfish, and trout, through systems of ordinary differential equations (ODEs) and partial differential equations (PDEs).
The initial mathematical objective is to compile a comprehensive set of relevant equations, along with a review of the current state of knowledge: existence of theoretical solutions (well-posedness), development of numerical schemes, and their implementation in one-dimensional and two-dimensional domains, as well as on graph structures.
Special attention will be given to cross-diffusion systems, particularly to prey-taxis type models. This thesis will contribute both methodologically and in terms of applied research to the modeling of spatial dynamics in predator-prey systems.
The results will help converge toward one or more models and associated equations that are consistent with empirical data from CEFE (Centre d'Écologie Fonctionnelle et Évolutive). We also plan to disseminate the findings through publications in academic journals and presentations at national and international conferences.

Contexte de travail

This project will be funded by the DyGéSTE program of the IMPT for a period of three years, with additional support for research resources. It will be developed at the Institut Montpelliérain Alexander Grothendieck.

The research may also include in-depth theoretical studies on lesser-explored equations, focusing on the existence of solutions, Turing instability analysis, and convergence of numerical schemes. These aspects could lead to collaborations with research teams in Toulouse (Ariane Trescases, Sepideh Mirrahimi) and Paris (Ayman Moussa, Laurent Desvillettes).

Contraintes et risques

-

Informations complémentaires

Master's degree in partial differential equations (PDE) analysis, with a strong theoretical background in the field and solid skills in numerical tools, particularly LaTeX and the Python programming language. An interest in biological models and dynamical systems is also expected.