Delay effect in models of population growth

Abstract

First, we systematize earlier results on the global stability of the model ẋ + μx = f(x(· - τ)) of population growth. Second, we investigate the effect of delay on the asymptotic behavior when the nonlinearity f is a unimodal function. Our results can be applied to several population models [Elements of Mathematical Ecology, 2001 [7] ; Appl. Anal. 43 (1992) 109-124; Math. Comput. Modelling, in press; Funkt. Biol. Med. 256 (1982) 156-164; Math. Comput. Modelling 35 (2002) 719-731; Mat. Stos. 6 (1976) 25-40] because the function f does not need to be monotone or differentiable. Specifically, our results generalize earlier result of [Delay Differential Equations with Applications in Population Dynamics, 1993], since our function f may not be differentiable. © 2004 Elsevier Inc. All rights reserved.