On the Solutions of a System of Third-Order Rational Difference Equations

Abstract

The structure of the solutions for the system nonlinear difference equations xn+1=ynyn-2/(xn-1+yn-2), yn+1=xnxn-2/(±yn-1±xn-2), n=0,1,…, is clarified in which the initial conditions x-2, x-1, x0, y-2, y-1, y0 are considered as arbitrary positive real numbers. To exemplify the theoretical discussion, some numerical examples are presented.

Global Dynamics of Higher-Order Exponential Systems of Difference Equations

“…Construction of Invariant Rectangle of Systems (11), (12), and (13) (11), (ii) system (12), and (iii) system (13) is bounded and persists.…”

“…where ( = 1, ⋅ ⋅ ⋅ , 4) and 0 , 0 are positive real numbers, and for more other interesting results on difference equations as well as systems of difference equation, we refer the reader to [11][12][13] and the references cited therein. Motivated by the above systemic studies, in this paper we aim to explore the dynamical properties of the following higher-order exponential systems of difference equations, which are natural extension of the work studied by Ozturk et al [4]:…”

“…The rest of this paper is organized as follows: Section 2 is about the study of boundedness and persistence of systems (11), (12), and (13). This also includes construction of invariant rectangle of these systems.…”

“…This also includes construction of invariant rectangle of these systems. Section 3 is about the uniqueness and existence of +V fixed point of systems (11), (12), and (13). Section 4 deals with the study of local stability, whereas in Section 5 we study the global dynamics of the unique +V fixed point of these systems.…”

“…Section 4 deals with the study of local stability, whereas in Section 5 we study the global dynamics of the unique +V fixed point of these systems. Section 6 deals with the study of rate of convergence of systems (11), (12), and (13). Brief conclusion is given in Section 7.…”