A global asymptotic stability condition for a Lotka–Volterra model with indirect interactions

Abstract

ABSTRACTA two-species Lotka–Volterra model extended with an arbitrary number of indirect interactions through diffusible and renewable compounds is presented in view of its considerable interest to the microbial community modelling. After the determination of the system’s fixed points and a short discussion over their local asymptotic stability, Lyapunov’s second method is applied to derive a sufficient condition of global asymptotic stability. Biologically, this condition indicates the necessity for one microbial type to show strong self-inhibition and the compounds to be quickly replaced.