Dynamics of rational difference equation Xn+1=α+βxn / A+Bxn+Cxn−k using mathematical and computational approach

Abstract

The main goal of this thesis is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation Xn+1=α+βxn / A+Bxn+Cxn−k, n= 0,1,2,... where the parameters α,β,A,B and C are non-negative real numbers with at least one parameter is non zero and the initial conditions x−k , x−k+1,...,x−1, x0 are non-negative real numbers with the solution is defined and k∈{1,2,3,...}. We give a detailed description of the semi-cycles of solutions, and determine conditions under which the equilibrium points are globally asymptotically stable.