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Title: Dynamics of rational difference equation Xn+1=α+βxn / A+Bxn+Cxn−k using mathematical and computational approach
Authors: Saleh, Mohammad
Alawneh, Abed Elrazzaq
Keywords: Differential dynamical systems - Mathematical models
Difference equations - Numerical solutions
Differential equations, Partial - Numerical solutions
Differential equations, Linear
Issue Date: 2007
Publisher: Birzeit University
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.
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