Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order
2018 ◽
Vol 2018
◽
pp. 1-6
◽
Keyword(s):
We study in this paper the following max-type system of difference equations of higher order: xn=max{A,yn-k/xn-1} and yn=max{B,xn-k/yn-1}, n∈{0,1,2,…}, where A≥B>0, k≥1, and the initial conditions x-k,y-k,x-k+1,y-k+1,…,x-1,y-1∈(0,+∞). We show that (1) if AB>1, then every solution of the above system is periodic with period 2 eventually. (2) If AB=1>B, then every solution of the above system is periodic with period 2k or 2 eventually. (3) If A=B=1 or AB<1, then the above system has a solution which is not periodic eventually.
2013 ◽
Vol 66
(11)
◽
pp. 2239-2250
◽
2020 ◽
Vol 5
(1)
◽
pp. 275-282
2009 ◽
Vol 2009
◽
pp. 1-11
◽
Keyword(s):
2005 ◽
Vol 50
(10-12)
◽
pp. 1725-1754
◽
2011 ◽
Vol 216
◽
pp. 50-55
◽