Global behavior of positive solutions of a third order difference equations system

2021/08/12 by Mai Nam Phong, Phong, Mai Nam
Mathematics · Medicine · #39A10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2108.05534

openalex publication_date 2021/08/12 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

\beginabstract In this paper, we consider the following system of difference equations x_n+1=α+\dfracy_n^py_n-2^p, y_n+1=α+ \dfracx_n^qx_n-2^q, n=0, 1, 2, ... where parameters α, p, q ∈ (0, ∞) and the initial values x_-i, y_-i are arbitrary positive numbers for i=-2,-1, 0. Our main aim is to investigate semi-cycle analysis of solutions of above system. Also, we study the boundedness of the positive solutions and the global asymptotic stability of the equilibrium point in case α>1, 0

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