MMN-4758
On the balancing-bilinear system of difference equations: solutions via some number sequences and global stability
Ahmed Ghezal; Imane Zemmouri;Abstract
In the current paper, we present a new class of systems called the Balancing-bilinear system of difference equations to investigate some theoretical proprieties. In this class of systems, the coefficients are allowed to depend on the Balancing sequence. One feature of this new class of systems is theoretically solvable in closed form. For this purpose, our interest is focused firstly to show that the solutions of this system are also related to Balancing numbers. As a consequence, we find that these solutions are also related to some number sequences (Pell numbers, Pell-Lucas numbers and Lucas-Balancing numbers). Secondly, we invest in the essential problems related to the Balancing-bilinear system, i.e. the global stability of positive solutions.
Vol. 26 (2025), No. 2, pp. 785-795