Global stability of discrete-time competitive population models

Baigent, Stephen and Hou, Zhanyuan (2017) Global stability of discrete-time competitive population models. Journal of Difference Equations with Applications, 23 (2017). ISSN 1023-6198 (print) 1563-5120 (online)

Abstract

We develop practical tests for the global asymptotic stability of interior fixed points for discrete-time competitive population models. Our method constitutes the extension to maps of the Split Lyapunov method developed for differential equations. We give ecologically-motivated sufficient conditions for global stability of an interior fixed point of a map of Kolmogorov form. We introduce the concept of a principal reproductive mode, which is linked to a normal at the interior fixed point of a hypersurface of vanishing weighted-average growth. Our method is applied to establish new global stability results for 3-species competitive systems of May-Leonard type, where previously only parameter values for local stability was known.

Documents
1227:6688
[thumbnail of Stability for discrete competitive models.pdf]
Preview
Stability for discrete competitive models.pdf - Published Version

Download (1MB) | Preview
Details
Record
View Item View Item