a1 School of Mathematical Sciences, Flinders University, Bedford Park, S.A. 5042.
It is shown that if intraspecific self-regulating negative feedback effects are strong enough such that a nontrivial steady state of a two species system is locally asymptotically stable, then time delays in the positive feedback as well as in other interspecific interactions cannot destabilise the system and hence delay induced instability leading to persistent oscillations is impossible whatever the magnitude of the time delays. A method is also proposed for an estimate of decay rate of perturbations.
(Received November 01 1982)
(Revised March 07 1983)