# American Institute of Mathematical Sciences

November  2013, 12(6): 2997-3012. doi: 10.3934/cpaa.2013.12.2997

## Bifurcations and periodic orbits in variable population interactions

 1 Department of Mathematics, Missouri State University, Springfield, MO 65897

Received  November 2012 Revised  February 2013 Published  May 2013

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.
Citation: Jorge Rebaza. Bifurcations and periodic orbits in variable population interactions. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2997-3012. doi: 10.3934/cpaa.2013.12.2997
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