Title: Behaviour of two-dimensional competitive system of nonlinear difference equations of higher order

Authors: Jerico B. Bacani; Julius Fergy T. Rabago

Addresses: Department of Mathematics and Computer Science, College of Science, University of the Philippines Baguio, Baguio City 2600, Benguet, Philippines ' Department of Mathematics and Computer Science, College of Science, University of the Philippines Baguio, Baguio City 2600, Benguet, Philippines

Abstract: We generalise a recent result of Mansour et al. (2012) and study other related systems that deal with the dynamics of a competitive population model described by a system of nonlinear difference equations. Particularly, we consider a discrete-competitive system of the form χn+1 = ƒ(χn−(2k−1),Yn−(k−1),Yn+1 = gn−(2k−1),Yn−(k−1)), n ∈ ℕ₀, where k ∈ ℕ and ƒ:ℝ \ Ƒƒ → ℝ and g: ℝ \ Ƒg → ℝ, where Ƒƒ and Ƒg denote the forbidden sets of ƒ and g, respectively. This work, in turn, generalises several other results on system of nonlinear difference equations. See, for example, the work of Alghamdi et al. (2013), Elsayed (2012), Ibrahim et al. (2015), Kurbanli (2011) and Touafek and Elsayed (2012). Furthermore, the one-dimensional case of the given system provides a generalisation of a series of paper of Elsayed on nonlinear difference equations.

Keywords: discrete dynamical system; nonlinear difference equation; form of solutions; convergence; periodicity; competitive system.

DOI: 10.1504/IJDSDE.2019.098409

International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.1, pp.14 - 43

Available online: 08 Mar 2019 *

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