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Solvability and semi‐cycle analysis of a class of nonlinear systems of difference equations
Author(s) -
Stević Stevo,
Tollu Durhasan T.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5600
Subject(s) - mathematics , nonlinear system , class (philosophy) , mathematical analysis , pure mathematics , combinatorics , physics , quantum mechanics , artificial intelligence , computer science
An analysis of semi‐cycles of positive solutions to eight systems of difference equations of the following formx n = a + p n − 1q n − 2p n − 1 + q n − 2,y n = a + r n − 1s n − 2r n − 1 + s n − 2, n ∈ N 0 , where a ∈ [0, + ∞ ), the sequences p n , q n , r n , s n are some of the sequences x n and y n , with positive initial values x − j , y − j , j = 1,2, is conducted in detail, and it is shown that these systems can be solved in closed‐form, which is the main result here. Two methods for showing the solvability are described.