How the Fractional-order Improve and Extend the Well-known Competitive Exclusion Principle in the Chemostat Model with n Species Competing for a Single Resource?
Sayed Sayari
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belvedere, Tunis El Manar university, Tunisia and Higher Institute of Environmental Technologies of Urban Planning and Building, 2 Rue de l'Artisanat Charguia 2, 2035 Tunis, Carthage university, Tunisia.
Miled El Hajji *
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belvedere, Tunis El Manar university, Tunisia.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a fractional-order mathematical model for n species competing, in a chemostat,
for a single resource is proposed. The global dynamics was studied using Lyapunov theory, for
any set of increasing growth functions. Obtained results generalize and improve the well-known
competitive exclusion principle in the chemostat, that one species will eliminate all other species.
Keywords: Chemostat model, competitive exclusion, fractional order, Caputo fractional derivative, nonlinear growth rate, equilibrium points, local and global stability.