Qualitative Analysis of Discrete Dynamical Systems Involving k-Mersenne Numbers

Qualitative Analysis of Discrete Dynamical Systems Involving k-Mersenne Numbers | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Qualitative Analysis of Discrete Dynamical Systems Involving k-Mersenne Numbers Amira Khelifa, Yacine Halim, Michal Fečkan, Turki D. Alharbi, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7123019/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Oct, 2025 Read the published version in Qualitative Theory of Dynamical Systems → Version 1 posted 11 You are reading this latest preprint version Abstract This paper studies the dynamics of a nonlinear difference system related to the k-Mersenne sequence a generalization of classical Mersenne numbers. By transforming the nonlinear system into a linear form, explicit solutions are obtained in terms of k-Mersenne numbers. The analysis establishes the global asymptotic stability of the system’s positive equilibrium and characterizes the convergence rate using the Jacobian’s spectral radius. Numerical examples confirm the theoretical findings and illustrate the system’s stability and behavior. MSC Classification: 39A10 , 40A05. General solution System of difference equations k-Mersenne sequence Stability Rate of convergence Full Text Additional Declarations No competing interests reported. Supplementary Files Khelifaetal.rar Cite Share Download PDF Status: Published Journal Publication published 22 Oct, 2025 Read the published version in Qualitative Theory of Dynamical Systems → Version 1 posted Editorial decision: Revision requested 17 Sep, 2025 Reviews received at journal 31 Jul, 2025 Reviews received at journal 27 Jul, 2025 Reviewers agreed at journal 23 Jul, 2025 Reviewers agreed at journal 23 Jul, 2025 Reviewers agreed at journal 22 Jul, 2025 Reviewers agreed at journal 16 Jul, 2025 Reviewers invited by journal 16 Jul, 2025 Editor assigned by journal 15 Jul, 2025 Submission checks completed at journal 15 Jul, 2025 First submitted to journal 14 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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