Dynamics of the modified Michaelis–Menten system

The theory of cooperative and competitive systems is used to study the dynamical behaviour of the modified Michaelis–Menten system. Conditions for convergence to equilibria and existence of stable closed orbits are given, improving previous results obtained in [R.A. Smith, Some modified Michaelis–Menten equations having stable closed orbits, Proc. Roy. Soc. Edinburgh Sect. A 109 (1988) 341–359].