## Abstract and Applied Analysis

### Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms

#### Abstract

We investigate global dynamics of the following systems of difference equations ${x}_{n+\mathrm{1}}={x}_{n}/({A}_{\mathrm{1}}+{B}_{\mathrm{1}}{x}_{n}+{C}_{\mathrm{1}}{y}_{n})$, ${y}_{n+\mathrm{1}}={y}_{n}^{\mathrm{2}}/({A}_{\mathrm{2}}+{B}_{\mathrm{2}}{x}_{n}+{C}_{\mathrm{2}}{y}_{n}^{\mathrm{2}})$, $n=\mathrm{0,1},\dots$, where the parameters ${A}_{\mathrm{1}}$, ${A}_{\mathrm{2}}$, ${B}_{\mathrm{1}}$, ${B}_{\mathrm{2}}$, ${C}_{\mathrm{1}}$, and ${C}_{\mathrm{2}}$ are positive numbers and the initial conditions ${x}_{\mathrm{0}}$ and ${y}_{\mathrm{0}}$ are arbitrary nonnegative numbers. This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space.

#### Article information

Source
Abstr. Appl. Anal., Volume 2017 (2017), Article ID 3104512, 19 pages.

Dates
Received: 1 April 2017
Accepted: 4 June 2017
First available in Project Euclid: 19 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1505786568

Digital Object Identifier
doi:10.1155/2017/3104512

Mathematical Reviews number (MathSciNet)
MR3686354

Zentralblatt MATH identifier
06929547

#### Citation

Hadžiabdić, V.; Kulenović, M. R. S.; Pilav, E. Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms. Abstr. Appl. Anal. 2017 (2017), Article ID 3104512, 19 pages. doi:10.1155/2017/3104512. https://projecteuclid.org/euclid.aaa/1505786568

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