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We show that the following two‐dimensional system of difference equations: xn+1=anxn+bnyn,yn+1=cnxn+dnyn,n∈N0, where (an)n∈N0 , (bn)n∈N0 , (cn)n∈N0 , and (dn)n∈N0 are periodic sequences, is solvable, considerably extending some results in… Click to show full abstract
We show that the following two‐dimensional system of difference equations: xn+1=anxn+bnyn,yn+1=cnxn+dnyn,n∈N0, where (an)n∈N0 , (bn)n∈N0 , (cn)n∈N0 , and (dn)n∈N0 are 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.
Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2019
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