Weak resilience of the chemostat model to a species invasion with non-autonomous removal rates

Térence Bayen (1) , Alain Rapaport (2) , Fatima Zahra Tani (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

In this paper, we study how resilience in the chemostat model with two species can be guaranteed in a weak sense in presence of a species invader. Doing so, we construct a time varying removal rate that allows the resident species to return an infinite number of times to its original density level, even though the invader can never be totally eradicated. Moreover, we prove that the time spent by the system with the resident density above or equal to its original level is of infinite measure introducing that way the concept of "weak resilience". Finally, under the conjecture that there exists an unique periodic solution of the system associated with such a time-varying removal rate, we show that every solution converges asymptotically to this periodic solution.

Mots clés: Non-autonomous Dynamics; Chemostat Model; Periodic systems; Asymptotically Periodic Solutions

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]; Biodiversité et Ecologie

Térence Bayen, Alain Rapaport, Fatima Zahra Tani. Weak resilience of the chemostat model to a species invasion with non-autonomous removal rates. 2019. ⟨hal-02068276⟩