Communications on Pure and Applied Analysis (CPAA)

Bifurcations and periodic orbits in variable population interactions

Pages: 2997 - 3012, Volume 12, Issue 6, November 2013      doi:10.3934/cpaa.2013.12.2997

       Abstract        References        Full Text (541.7K)       Related Articles       

Jorge Rebaza - Department of Mathematics, Missouri State University, Springfield, MO 65897, United States (email)

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.

Keywords:  Variable Population models, conditional interactions, stability, bifurcations.
Mathematics Subject Classification:  Primary: 37N25, 58F17; Secondary: 92D25.

Received: November 2012;      Revised: February 2013;      Available Online: May 2013.