Bifurcation analysis of the flour beetle population growth equations

Abstract

In this article, we study a discrete delayed flour beetle population equation. Firstly, we study the existence of period-doubling bifurcation and Neimark–Sacker bifurcations for the system by analysing its characteristic equations. Secondly, we investigate the direction of the two bifurcations and the stability of the bifurcation periodic solutions by using normal form theory. Finally, some numerical simulations are carried out to support the analytical results.

Keywords:

• difference equation
• stability
• period-doubling bifurcation
• Neimark–Sacker bifurcation
• Jury's conditions

AMS Subject Classification::

• 39A11
• 34K18
• 37C75

Acknowledgements

The authors are grateful to anonymous referees for their excellent suggestions, which greatly improved the presentation of the paper. This work was partially supported by the National Natural Science Foundation of China (No.10671047) and by the Science Research Foundation in Harbin Institute of Technology (200713).