Global dynamics of Nicholson's blowflies equation revisited: Onset and termination of nonlinear oscillations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Shu, Hongying¹  Wang, Lin¹  Wu, Jianhong² 

[1] Univ New Brunswick, Dept Math & Stat, Fredericton, NB E3B 5A3, Canada

[2] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada

关键词: Nicholson's blowflies equation;    Maturation delay;    Hopf bifurcation;    Hopf branch;    Multiple stable periodic solutions;   

DOI  :  10.1016/j.jde.2013.06.020

来源: Elsevier

【 摘 要 】

We revisit Nicholson's blowflies model with natural death rate incorporated into the delay feedback. We consider the delay as a bifurcation parameter and examine the onset and termination of Hopf bifurcations of periodic solutions from a positive equilibrium. We show that the model has only a finite number of Hopf bifurcation values and we describe how branches of Hopf bifurcations are paired so the existence of periodic solutions with specific oscillation frequencies occurs only in bounded delay intervals. The bifurcation analysis and the Matlab package DDE-BIFTOOL developed by Engelborghs et al. guide some numerical simulations to identify ranges of parameters for coexisting multiple attractive periodic solutions. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free