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Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

Perturbations in dynamical systems for EFL learning

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pp. 1–10Online FirstJuly 2026DOI: 10.47974/JIM-2459XML
Received:
01 Aug 2025
Published Online:
01 Jul 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2459
Pages:
1–10

Abstract

We study mathematical perturbed equations that can be used to describe how learner motivation, engagement, and proficiency develop together in English as a Foreign Language (EFL) contexts. The basic system uses first-order ordinary differential equations to show how motivation and engagement influence each other, while proficiency grows in a logistic way but also declines if not reinforced. To try to make the system closer to classroom situations, we add a small perturbation term that represents changes caused by teaching methods or other external factors. We analyze the stability and behavior of the system. Numerical examples show that the equations remain stable even under small perturbations. Our results suggest that mathematical systems with perturbations provide useful tools for understanding how motivation and learning progress in second language acquisition.

Keywords

Subject Classifications

34C2934E1034D2091F9997C70

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