Delay effect in models of population growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:305

Article

Giang, DV ; Lenbury, Y ; Seidman, TI

关键词: delay differential equations;    comparison theorem;    omega-limit set of a persistent solution;    one-parameter semi-group;    convergence to equilibrium;    Nicholson's blowfly model;    periodic solutions;   

DOI  :  10.1016/j.jmaa.2004.12.018

来源: Elsevier

【 摘 要 】

First, we systematize earlier results on the global stability of the model x + mu x = f (x((.) - iota)) 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. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free