Coexistence of three predators competing for a single biotic resource

Claude Lobry (1) , Tewfik Sari (1, 2) , Karim Yadi (3)

1 MERE - Water Resource Modeling
2 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
3 LSDA - Laboratoire Systèmes Dynamiques et Applications

We construct a model of competition of three consumers for one single biotic resource ; simulations show that the three species coexist. Using singular perturbations theory we sketch a mathematical proof for this coexistence. The main mathematical tool used is an extension of the Pontryagin-Rodygin theorem on the ''slow'' motion of a ''slow-fast'' differential system when the ''fast'' motion possesses a stable limit cycle. The mathematical analysis is done within the framework of Non Standard Analysis.

Mots clés: SYSTEME DIFFERENTIEL; COEXISTENCE DES ESPECES; SPECIES COEXISTENCE; DIFFERENTIAL SYSTEM; ECOLOGIE

Domaines: Systèmes dynamiques [math.DS]

Claude Lobry, Tewfik Sari, Karim Yadi. Coexistence of three predators competing for a single biotic resource. Jean Lévine and Philippe Müllhaupt. Advances in the Theory of Control, Signals and Systems with Physical Modeling - Part III, Springer, pp.309-321, 2011, Lecture Notes in Control and Information Sciences - 407, 978-3-642-16134-6. ⟨10.1007/978-3-642-16135-3_25⟩. ⟨hal-00486459⟩