A STUDY ON A SOLVABLE TWO-DIMENSIONAL SYSTEM OF FOURTH-ORDER DIFFERENCE EQUATIONS

Abstract

This paper investigates a nonlinear system of rational difference
equations of order four, given by:
xn+1 =
ynyn−3
axn−2 − byn−3,
yn+1 =
xnxn−3
cyn−2 − dyn−3,
where n ∈ N0, and a, b, c, and d are real parameters. The initial conditions
x−3, x−2, x−1, x0, y−3, y−2, y−1, and y0 are nonzero real numbers.
The study aims to derive explicit solutions and establish conditions for existence
and uniqueness, and analyze the qualitative dynamics, including stability and
asymptotic behavior. These results provide new insights into the complex
interplay between system parameters and initial conditions.