Abstract:

     This paper addressed a type of chemostat model with linear variable yield and Beddington-DeAngelis type functional response. We deliberately analyze the existence and local asymptotic stability of its equilibrium.We also prove that the washout equilibrium  E₀ is globally asymptotically stable using Liapunov-LaSalle invariant principle. E₁₀ and E₂₀ are globally asymptotically stable. Numerical simulations are presented to demonstrate the global asymptotic stability of four equilibrium E₀, E₁₀, E₂₀, E_* .

Key words: Beddington-DeAngelis functional response, chemostat, Liapunov-LaSalle invariant principle, stability