Dynamical analysis of a two prey-one predator system with quadratic self interaction

I. Kusbeyzi Aybar, O.O. Aybar, M. Dukarić and B. Ferčec

Applied Mathematics and Computation, 2018, vol. 333, issue C, 118-132

Abstract: In this paper we investigate the dynamical properties of a two prey-one predator system with quadratic self interaction represented by a three-dimensional system of differential equations by using tools of computer algebra. We first investigate the stability of the singular points. We show that the trajectories of the solutions approach to stable singular points under given conditions by numerical simulation. Then, we determine the conditions for the existence of the invariant algebraic surfaces of the system and we give the invariant algebraic surfaces to study the flow on the algebraic invariants which is a useful approach to check if Hopf bifurcation exists.

Keywords: Predator-prey; Stability analysis; Hopf bifurcation (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:333:y:2018:i:c:p:118-132

DOI: 10.1016/j.amc.2018.03.123

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