Qualitative analysis of solutions to a general class of nonlinear difference equations with applications

Authors

• Osama Moaaz, Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaFollow
• Mohamed F. Abouelenein, Department of Insurance and Risk Management, College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaFollow
• Mona Anis, Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, EgyptFollow

Abstract

This work examines the qualitative behavior of a general class of difference equations. We establish criteria guaranteeing the stability, periodicity, and boundedness of the solutions of the equation under consideration. In addition, we identify its invariant intervals. The theoretical results are subsequently applied to various special cases, among them the May--Host model. Numerical simulations are presented to demonstrate the dynamics of the solutions and to validate the theoretical analysis.

Recommended Citation

Moaaz, Osama; Abouelenein, Mohamed F.; and Anis, Mona (2026) "Qualitative analysis of solutions to a general class of nonlinear difference equations with applications," Mathematical Modelling and Numerical Simulation with Applications: Vol. 6: Iss. 2, Article 1.
DOI: https://doi.org/10.53391/2791-8564.1025
Available at: https://mmnsa.researchcommons.org/journal/vol6/iss2/1