GLOBAL STABILITY IN THE DEGN-HARRISON MODEL

BENEDETTA LISENA

Abstract


The main goal of this paper is to investigate the global dynamics of the model proposed by Degn and Harrison to explain the oscillations in continuous bacterial cultures. We establish suitable conditions on the parameters ensuring the global asymptotic stability of the unique equilibrium. The technique of the invariant rectangles in the phase-space and the Lyapunov method are used. Our investigation confers a theoretical background for the numerical and experimental results in [6].

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