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On a class of systems of rational second‐order difference equations solvable in closed form
Author(s) -
Stević Stevo
Publication year - 2020
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.5809
Subject(s) - mathematics , class (philosophy) , transformation (genetics) , nonlinear system , order (exchange) , pure mathematics , mathematical analysis , biochemistry , chemistry , physics , finance , quantum mechanics , artificial intelligence , computer science , economics , gene
We show that the following nonlinear system of difference equationsx n + 1 = a y n + c y ny n − b x n − 1,y n + 1 = b x n + d x nx n − a y n − 1, n ∈ N 0 , where parameters a , b , c , d and initial values x −1 , x 0 , y −1 , y 0 are real numbers, is solvable in closed form, considerably generalizing some recent results. To do this, we use the method of transformation along with several tricks, transforming the system to some known solvable difference equations, by use of which we obtain some closed‐form formulas for general solution to the system. The following five cases are considered separately: (1) c =0; (2) d =0; (3) a =0; (4) b =0; and (5) a b c d ≠0.