Bifurcation analysis on a discrete model of Nicholson's blowflies

Abstract

In this paper, the discrete Nicholson's blowflies model with delay is considered. First, the stability of the equilibria of the system is investigated by analyzing the characteristic equation and then the existence of fold and Neimark–Sacker bifurcations are verified. Subsequent to that, the direction and stability of the bifurcation are determined by using the normal form theory and center manifold theorem. Finally, some numerical simulations are carried out in order to support the results of mathematical analysis.

Keywords:

• discrete Nicholson's blowflies
• fold bifurcation
• Neimark–Sacker bifurcation

Acknowledgements

The authors are grateful to the anonymous referee for her or his helpful comments and valuable suggestions. This research is supported by the National Natural Science Foundation of China (No. 10771045) and Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050213002).