Dynamics of positive solutions of a three dimensional higher order system of difference equations

Hassani, Murad Khan and Yazlik, Yasin and Touafek, Nouressadat (2024) Dynamics of positive solutions of a three dimensional higher order system of difference equations. Miskolc Mathematical Notes, 25 (2). pp. 713-735. ISSN 1787-2413

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Abstract

In this paper, we study the global behavior of positive solutions of the following system of difference equations xn+1 = A + yn yn−k,yn+1 = A + zn zn−k,zn+1 = A + xn xn−k,n ∈ ℕ0, where the parameter A > 0, the initial values x−i,y−i,z−i, i ∈{0,1,2,…,k}, are arbitrary positive real number and k ∈ ℕ. Moreover, we provide semi-cycle analysis of positive solutions to the above system of difference equations. Finally, we also give some numerical examples which support our analytical results.

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