GLOBAL STABILITY IN DELAY-DIFFERENTIAL SYSTEMS WITHOUT DOMINATING INSTANTANEOUS NEGATIVE FEEDBACKS

Most of the global stability or convergence results appearing so far f or delayed Lotka-Volterra-type systems or other delay differential sys tems require that the instantaneous negative feedbacks dominate both d elayed feedback and interspecific interactions. Such a requirement is rarely met in real systems since feedbacks are generally delayed. This leads to the long standing question: Under what conditions will the g lobal stability of a nonnegative steady state of a differential delay system persist when time delays involved in some part of the negative feedbacks are small enough? This paper presents a partial answer to th is open question. Roughly, our results show that if the delay differen tial system remains dissipative when delays are introduced, then the a bove open question has an affirmative answer. Our results also improve some recent findings. (C) 1995 Academic Press, Inc.