A Maple program to the Analysis of Equilibrium Points in Social Media Addiction Model

Year 2025, Volume: 18 Issue: 1, 115 - 128, 28.03.2025

Mehmet Kocabıyık

https://doi.org/10.18185/erzifbed.1514507

Abstract

In today's world, the relationship between social media and the internet is becoming increasingly important. Therefore, there is a need to determine the level of social media addiction. In addition to expressing social media addiction mathematically, equilibrium point analyzes of such equation systems also illuminate the extent and impact of addiction. This study focuses on such a model. Discretization of the model was achieved using the non-standard finite difference method. Equilibrium points were identified and analyzed using the Maple software package. In addition, Maple working codes are also given in the article, contributing to the literature in this field.

Keywords

Maple package programming, Equilibrium point, Social media addiction model, Numerical Analysis.

References

• [1] Kuss, D. J., Griffiths, M. D., (2017) Social networking sites and addiction: Ten lessons learned, International Journal of Environmental Research and Public Health, 14(3), 311.
• [2] Turel, O., He, Q., Xue, G., Xiao, L., Bechara, A., (2014) Examination of neural systems sub-serving Facebook “addiction”, Psychological Reports, 115(3), 675-695.
• [3] Young, K. S., (2017) The evolution of internet addiction disorder, Internet addiction: Neuroscientific approaches and Therapeutical implications including smartphone addiction, 3-18.
• [4] Andreassen, C. S., Pallesen, S., Griffiths, M. D., (2016) The relationship between addictive use of social media, narcissism, and self-esteem: Findings from a large national survey, Addictive Behaviors, 64, 287-293.
• [5] Bian, M., Leung, L., (2017) Linking loneliness, shyness, smartphone addiction symptoms, and patterns of smartphone use to social capital, Social Science Computer Review, 33(1), 61-79.
• [6] Ishaku, A., Musa, B. S., Sanda, A., Bakoji, A. M., (2018) Mathematical assessment of social media impact on academic performance of students in higher institution, IOSR J. Math, 2018, 72-79.
• [7] Simsek, A., Elciyar, K., Kizilhan, T., (2019) A comparative study on social media addiction of high school and university students, Contemporary educational technology, 10(2), 106-119.
• [8] Shutaywi, M., Rehman, Z. U., Shah, Z., Vrinceanu, N., Jan, R., Deebani, W., Dumitrascu, O., (2023) Modeling and analysis of the addiction of social media through fractional calculus, Frontiers in Applied Mathematics and Statistics, 9, 1210404.
• [9] Guo, Y., Li, T., (2020) Optimal control and stability analysis of an online game addiction model with two stages, Mathematical Methods in the Applied Sciences, 43(7), 4391-4408.
• [10] Alemneh, H. T., Alemu, N. Y., (2020) Mathematical modeling with optimal control analysis of social media addiction, Journal of Applied Mathematics and Physics, 8, 2136-2155.
• [11] Savci, M., Tekin, A., Elhai, J. D., (2022) Prediction of problematic social media use (PSU) using machine learning approaches, Current Psychology, 41(5), 2755-2764.
• [12] Çiftci, N., Yıldız, M., (2023) The relationship between social media addiction, happiness, and life satisfaction in adults: analysis with machine learning approach, International Journal of Mental Health and Addiction, 21(5), 3500-3516.
• [13] Shao, Y. J., Zheng, T., Wang, Y. Q., Liu, L., Chen, Y., Yao, Y. S., (2018) Internet addiction detection rate among college students in the People’s Republic of China: A meta-analysis, Child and Adolescent Psychiatry and Mental Health, 12, 1-10.
• [14] Kocabıyık, M., Ongun, M. Y., Çetinkaya, İ. T., (2021) Standart olmayan sonlu fark metodu ile dağılımlı mertebeden SVIR modelinin nümerik analizi, Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 23(2), 577-591.
• [15] İğret Araz, S., (2021) Numerical approximation with Newton polynomial for the solution of a tumor growth model including fractional differential operators, Erzincan University Journal of Science and Technology, 14(1), 249-259. https://doi.org/10.18185/erzifbed.753464
• [16] Kocabıyık, M., Ongun, M. Y., (2022) Construction of a distributed order smoking model and its nonstandard finite difference discretization, AIMS Mathematics, 7(3), 4636-4654. https://doi:10.3934/math.2022258
• [17] Kocabıyık, M., (2022) Nonstandard Discretization and Stability Analysis of a novel type Malaria-Ross Model, Journal of the Institute of Science and Technology, 12(2), 1023-1033. https://doi.org/10.21597/jist.1026364
• [18] Melkamu, B., Mebrate, B., (2022) A Fractional Model for the Dynamics of Smoking Tobacco Using Caputo–Fabrizio Derivative, Journal of Applied Mathematics, 2022(1), 2009910.
• [19] Yiğider, M., Okur, S., (2023) Numerical Solution for Time-Fractional Murray Reaction-Diffusion Equations via Reduced Differential Transform Method, Erzincan University Journal of Science and Technology, 16(1), 120-137. https://doi.org/10.18185/erzifbed.1217232
• [20] Kocabıyık, M., Ongun, M. Y., (2023) Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models, Gazi University Journal of Science, 36(4), 1675-1691. https://doi.org/10.35378/gujs.1027381
• [21] Öztürk, Z., Bilgil, H., Sorgun, S., (2024) A new application of fractional glucose-insulin model and numerical solutions, Sigma Journal of Engineering and Natural Sciences, 42(2), 407-413.
• [22] Caputo, M., (1969) Elasticita e dissipazione, Zanichelli.
• [23] Caputo, M., (1995) Mean fractional-order-derivatives differential equations and filters, Annali dell’Universita di Ferrara, 41(1), 73-84.
• [24] Caputo, M., (2001) Distributed order differential equations modelling dielectric induction and diffusion, Fractional Calculus and Applied Analysis, 4(4), 421-442.
• [25] Mickens, R. E., (1989) Exact solutions to a finite‐difference model of a nonlinear reaction‐advection equation: Implications for numerical analysis, Numerical Methods for Partial Differential Equations, 5(4), 313-325.
• [26] Mickens, R. E., (1994) Nonstandard finite difference models of differential equations, World scientific.
• [27] Çetinkaya, İ. T., (2023) An Application of Nonstandard Finite Difference Method to a Model Describing Diabetes Mellitus and Its Complications, Journal of New Theory, (45), 105-119.
• [28] Podlubny, I., (1999) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Vol. 198), Elsevier.
• [29] Dorciak L., (1994) Numerical models for simulation the fractional-order control systems, UEF-04-94, The Academy of Sciences, Institute of Experimental Physic, Kosiice, Slovak Republic.
• [30] Meerschaert, M. M., Tadjeran, C., (2004) Finite difference approximations for fractional advection–dispersion flow equations, Journal of computational and applied mathematics, 172(1), 65-77.
• [31] Butcher, J. C. (1966). On the convergence of numerical solutions to ordinary differential equations. Mathematics of Computation, 20(93), 1-10.