Stability and invariant manifolds of a generalized Beddington host-parasitoid model

Abstract

We will investigate the stability and invariant manifolds of a new discrete host-parasitoid model. It is a generalization of the Beddington–Nicholson–Bailey model. Our study establishes analytically, for the first time, the stability of the coexistence fixed point.

Keywords:

• host-parasitoid
• Beddington
• Nicholson–Bailey
• stability
• centre manifold

AMS Subject Classification::

• 39A11
• 92D25

Acknowledgements

The first author thanks the financial support from TUBITAK for his stay at Trinity University during the period this paper was written.

Funding

This work was supported by the Scientific & Technological Research Council of Turkey (TUBITAK).