Asymptotic behavior of a new class of nonlinear rational difference equations. (English) Zbl 1489.39011

Moaaz, Osama; Elabbasy, Elmetwally M.; Mahjoub, Hamida

Rocky Mt. J. Math. 51, No. 5, 1781-1792 (2021).

Summary: This paper is concerned with the asymptotic behavior of solutions of a new class of the nonlinear rational difference equations. We establish new criteria for stability (local and global) and boundedness of solutions of the studied equation. Moreover, we investigate the periodic character (periodic two and three) of the solutions of these equations, by using new techniques. Finally, we give some interesting examples in order to verify our results.

MSC:

39A20	Multiplicative and other generalized difference equations
39A23	Periodic solutions of difference equations
39A30	Stability theory for difference equations

Keywords:

difference equations; equilibrium points; local stability; global stability; periodic solution

References:

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