Bifurcations and periodic orbits in variable population interactions

Abstract

Variable population interactions with harvesting on one of the species are studied. Existence and stability of equilibria and existence of periodic solutions are established, existence of some bifurcation phenomena are analytically and numerically studied, explicit threshold values are computed to determine the kind of interaction (mutualism, competition, host-parasite) between the species, and several numerical examples are provided to illustrate the main results in this work. A brief discussion on the influence of the harvesting function on the dynamics of the model is also included. Hopf bifurcations and periodic solutions are found for the first time in this kind of models.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.3934/cpaa.2013.12.2997

Keywords

stability, bifurcations, variable population models, conditional interactions

Publication Date

2013

Journal Title

Communications on Pure & Applied Analysis

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