Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610183 | Journal of Differential Equations | 2013 | 22 Pages |
Abstract
We revisit Nicholsonʼs 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hongying Shu, Lin Wang, Jianhong Wu,