Global stability for Michaelis-Menten single-species growth equations (Q2717969)

The author investigates sufficient conditions for the global stability of the positive equilibrium \(N^*=1\) of Michaelis-Menten single-species growth equations of the form NEWLINE\[NEWLINEN'(t)=r(t)N(t) \sum _{i=1}^{n} {a_i (1-N(t-\tau_i)) \over {(1+c_i)(1+c_iN(t-\tau_i))}}.NEWLINE\]NEWLINE These conditions generalize and improve the result of \textit{J. Yu} [Sci. China, Ser. A 39, No. 3, 225-237 (1996; Zbl 0861.34047)] and the result of \textit{V. L. Kocić} and \textit{G. Ladas} [Proc. Am. Math. Soc. 115, No. 4, 1083-1088 (1992; Zbl 0756.39005)].