In this paper, the circular system of Riccati type complex difference equations of the form
𝑢(𝑗)𝑛+1=𝑎𝑗𝑢(𝑗−1)𝑛+𝑏𝑗𝑐𝑗𝑢(𝑗−1)𝑛+𝑑𝑗
,𝑛=0,1,2,⋯,𝑗=1,2,⋯,𝑘
where un(0) := un(k) for all n, is investigated. First, the forbidden
set of the equation is given. Then the solvability of the system is examined
and then the expression of the solutions are given in terms of their initial
values. Next, the asymptotic behaviour of the solutions is studied. Finally, in
case of negative Riccati real numbers
𝑅𝑗:=𝑎𝑗𝑑𝑗−𝑏𝑗𝑐𝑗[𝑎𝑗+𝑑𝑗]2
,𝑗∈―――1,𝑘,it
is shown that there exists a unique positive fixed point which attracts all
solutions starting from positive states.
Author(s) Details
George L. Karakostas
Department of Mathematics, University of Ioannina, Ioannina
45110, Greece.
Please see the book here:- https://doi.org/10.9734/bpi/rumcs/v8/3703G
