What question did this study set out to answer?

This work aims to explore the qualitative behavior of nonlinear difference equations and establish criteria for their solutions.

June 27, 2026

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

Key Points

This work aims to explore the qualitative behavior of nonlinear difference equations and establish criteria for their solutions.
Analyzed a general class of difference equations to determine stability and periodicity criteria.
Identified invariant intervals and applied results to specific models, including the May-Host model.
Conducted numerical simulations to illustrate the dynamics and validate theoretical findings.
Established criteria that guarantee stability, periodicity, and boundedness of solutions.
Demonstrated through numerical simulations the dynamics align with theoretical predictions.
Identified invariant intervals crucial for understanding solution behavior.

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.

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

Key Points

Abstract

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