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Two‐dimensional solvable system of difference equations with periodic coefficients
Author(s) -
Stević Stevo
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.5780
Subject(s) - mathematics , period (music) , periodic system , mathematical analysis , periodic sequence , value (mathematics) , pure mathematics , statistics , physics , acoustics
We show that the following two‐dimensional system of difference equations:x n + 1 =a nx n+b ny n,y n + 1 =c nx n+d ny n, n ∈ N 0 , where( a n ) n ∈ N 0,( b n ) n ∈ N 0,( c n ) n ∈ N 0, and( d n ) n ∈ N 0are periodic sequences, is solvable, considerably extending some results in the literature. In the case when all these four sequences are periodic with period 2 or with period 3, we present closed‐form formulas for the general solutions to the corresponding systems of difference equations. Some comments regarding theoretical and practical solvability of the system, connected to the value of the period of the sequences, are given.