Asymptotic behavior of nonlinear compartmental systems: nonoscillation and stability

Abstrurci-This paper di.9cwm propertics related to the stabiity of a class of nonliuear compartmental systems. SpecificaUy, mathematical con-ditions which guarantee Qe same qualitative behavior inherent in linear compartmental systenw are considered. We first consider the nonoscilla-tory property of solutions and show that the system bas no periodic oscillation under a mild condition. ‘Ibe result is then used to derive a necessary and sufficient condition for every solution to converge to a set of equilibrium points which may depend both on the input and the initial stati. A sufficient condition is also given for an equifiirium state to depend only on the input. The asymptotic behavior of the free system9 is also considered, and a sufficient condition is given for the origin to be globally asymptoticaNy stable. Furthermore, for a closed compartmental system it is shown that for each given initial state, unique equilibrium state, if it exisQ, depends only on the total sum of the components of the initial state. Finally a sufficient condition is given for solutions to converge to th