1. Home
  2. Journals
  3. International Social Science Research and Review
  4. Articles In Press
  Submit Manuscript

Research Article | DOI: https://doi.org/ISSRR-RA-25-017

Analysis and control of a Dynamic Model Involving Students Anxiety towards Mathematics

Lakshmi. N. Sridhar *

Chemical Engineering Department University of  Puerto Rico Mayaguez  ,United States of America

*Corresponding Author: Lakshmi. N. Sridhar,Chemical Engineering Department University of Puerto Rico Mayaguez ,United States of America

Citation: Lakshmi. N. Sridhar (2025). Analysis and control of a Dynamic Model Involving Students Anxiety towards Mathematics, J International Social Science Research and Review. 2 (3), DOI: ISSRR-RA-25-017.

Copyright: Lakshmi. N. Sridhar, et al © (2025). This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Received: 31 July 2025 | Accepted: 05 August 2025 | Published: 19 August 2025

Keywords: bifurcation; optimization; control; mathematics; hopf

Abstract

Anxiety towards mathematics is the most common problem for many students in several universities. In this study, bifurcation analysis and multiobjective nonlinear model predictive control (MNLMPC) calculations are performed on a dynamic model involving students’ anxiety towards mathematics. Bifurcation analysis is a powerful mathematical tool used to deal with the nonlinear dynamics of any process. Several factors must be considered, and multiple objectives must be met simultaneously. The MATLAB program MATCONT was used to perform the bifurcation analysis. The MNLMPC calculations were performed using the optimization language PYOMO   in conjunction with the state-of-the-art global optimization solvers IPOPT and BARON.The bifurcation analysis reveals a branch point and a Hopf bifurcation point, which leads to a limit cycle. This Hopf point was eliminated using an activation factor that involves the tanh function. The branch point enables the multiobjective nonlinear model predictive control calculations to converge to the Utopia point, which is the best solution.

References

  1. Mohamed, S. H. & Tarmizi, R. A. Anxiety in mathematics learning among secondary school learners: A comparative study between Tanzania and Malaysia. Proc. Soc. Behav. Sci. 8, 498–504 (2010).
    View at Publisher | View at Google Scholar
  2. Akin, A. & Kurbanoglu, I. N. The relationships between math anxiety, math attitudes, and self-efficacy: A structural equation model. Stud. Psychol. 53(3), 263 (2011).
    View at Publisher | View at Google Scholar
  3. Maria de Lourdes, M., Monteiro, V. & Peixoto, F. Attitudes towards mathematics: Effects of individual, motivational, and social support factors. Child Dev. Res. 2012 (2012).
    View at Publisher | View at Google Scholar
  4. Hoorfar, H. & Taleb, Z. Correlation between mathematics anxiety with metacognitive knowledge. Proc. Soc. Behav. Sci. 182, 737–741 (2015).
    View at Publisher | View at Google Scholar
  5. Getahun, D. A., Adamu, G., Andargie, A. & Mebrat, J. D. Predicting mathematics performance from anxiety, enjoyment, value, and self-efficacy beliefs towards mathematics among engineering majors. Bahir Dar J. Educ. 16, 1 (2016).
    View at Publisher | View at Google Scholar
  6. Zakaria, E. & Syamaun, M. The effect of realistic mathematics education approach on students’ achievement and attitudes towards mathematics. Math. Educ. Trends Res. 1(1), 32–40 (2017).
    View at Publisher | View at Google Scholar
  7. Mazana, Y.M., Montero, C.S. & Olifage, C.R. Investigating Students’ Attitude Towards Learning Mathematics (2019).
    View at Publisher | View at Google Scholar
  8. Mazana, M. Y., Montero, C. S. & Casmir, R. O. Assessing students’ performance in mathematics in Tanzania: the teacher’s perspective.Int. Electron. J. Math. Educ. 15(3), em0589 (2020).
    View at Publisher | View at Google Scholar
  9. Teklu, S. W. & Terefe, B. B. Mathematical modeling analysis on the dynamics of university students animosity towards mathematics with optimal control theory. Sci. Rep. 12(1), 1–19 (2022).
    View at Publisher | View at Google Scholar
  10. Teklu, S. W. Analysis of fractional order model on higher institution students’ anxiety towards mathematics with optimal control theory. Sci. Rep. 13(1), 6867 (2023).
    View at Publisher | View at Google Scholar
  11. Dhooge, A., Govearts, W., and Kuznetsov, A. Y., MATCONT: “A Matlab package for numerical bifurcation analysis of ODEs”, ACM transactions on Mathematical software 29(2) pp. 141-164, 2003.
    View at Publisher | View at Google Scholar
  12. Dhooge, A.,W. Govaerts; Y. A. Kuznetsov, W. Mestrom, and A. M. Riet , “CL_MATCONT”; A continuation toolbox in Matlab, 2004.
    View at Publisher | View at Google Scholar
  13. Kuznetsov,Y.A. “Elements of applied bifurcation theory” .Springer,NY, 1998.
    View at Publisher | View at Google Scholar
  14. Kuznetsov,Y.A.(2009).”Five lectures on numerical bifurcation analysis” ,Utrecht University,NL., 2009.
    View at Publisher | View at Google Scholar
  15. Govaerts, w. J. F., “Numerical Methods for Bifurcations of Dynamical Equilibria”, SIAM, 2000.
    View at Publisher | View at Google Scholar
  16. Dubey S. R. Singh, S. K. & Chaudhuri B. B. 2022 Activation functions in deep learning: A comprehensive survey and benchmark. Neurocomputing, 503, 92-108. https://doi.org/10.1016/j.neucom.2022.06.111
    View at Publisher | View at Google Scholar
  17. Kamalov A. F. Nazir M. Safaraliev A. K. Cherukuri and R. Zgheib 2021,
    View at Publisher | View at Google Scholar
  18. Szandała, T. 2020, Review and Comparison of Commonly Used Activation Functions for Deep Neural Networks. ArXiv. https://doi.org/10.1007/978-981-15-5495-7
    View at Publisher | View at Google Scholar
  19. Sridhar. L. N. 2023 Bifurcation Analysis and Optimal Control of the Tu­mor Macrophage Interactions. Biomed J Sci & Tech Res 53(5). BJSTR. MS.ID.008470.DOI: 10.26717/BJSTR.2023.53.008470
    View at Publisher | View at Google Scholar
  20. Sridhar LN. Elimination of oscillation causing Hopf bifurcations in engineering problems. Journal of Applied Math. 2024b; 2(4): 1826.
    View at Publisher | View at Google Scholar
  21. Flores-Tlacuahuac, A. Pilar Morales and Martin Riveral Toledo; “Multiobjective Nonlinear model predictive control of a class of chemical reactors” . I & EC research; 5891-5899, 2012.
    View at Publisher | View at Google Scholar
  22. Hart, William E., Carl D. Laird, Jean-Paul Watson, David L. Woodruff, Gabriel A. Hackebeil, Bethany L. Nicholson, and John D. Siirola. “Pyomo – Optimization Modeling in Python” Second Edition. Vol. 67.
    View at Publisher | View at Google Scholar
  23. Wächter, A., Biegler, L. “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming”. Math. Program. 106, 25–57 (2006). https://doi.org/10.1007/s10107-004-0559-y
    View at Publisher | View at Google Scholar
  24. Tawarmalani, M. and N. V. Sahinidis, “A polyhedral branch-and-cut approach to global optimization”, Mathematical Programming, 103(2), 225-249, 2005
    View at Publisher | View at Google Scholar
  25. Sridhar LN. (2024)Coupling Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control. Austin Chem Eng. 2024; 10(3): 1107.
    View at Publisher | View at Google Scholar
  26. Upreti, Simant Ranjan(2013); Optimal control for chemical engineers. Taylor and Francis.
    View at Publisher | View at Google Scholar
img

Harry Brooks

journal of Clinical Case Studies and Review Reports. I would be very delighted to submit my testimonial regarding the reviewer board and the editorial office.the reviewer board were accurate and helpful regarding anu modifications for my manuscript,and the editorial office were very helpful and supportive in contacting and monitoring with any update and offering help.it was my pleasure to contribute with your promising journal and i am looking forward for more collaboration.

img

Mark

My testimonial covering : the peer review process is qucick and effective,the support from the editorial office is very professional and friendly, quality of the Clinical Case Studies and Review Reports is scientific and publishers research.

img

Sinisa franjic

i would like to thank the editorial team for their timely responses and consideration in the publication of my paper . I would encourage to publish there research in ScienceFrontier.

img

Ritu Tiwari

I am pleased to submit my testimonials regarding the reviewer board and the editorial office. As a peer reviewer for the manuscript titled “A Novel Dissolution Method for Simultaneous Estimation of sennoside A and Sennoside B in Senna Tablet,” I was consistently impressed by the reviewers’ thorough analysis, insightful feedback, and unwavering commitment to enhancing the quality of the work. Their reviews were comprehensive and characterized by a respectful and collaborative approach, providing valuable suggestions that significantly improved the paper's outcome. Their dedication to the peer review process demonstrated their expertise and steadfast pursuit of excellence.

img

Qader Bawerdi

With all due respect, I would like to express my opinion on the peer review, editorial support, and the quality of the journal as follows: The peer review was conducted quickly and with great care, and my article was accepted for publication in less than a week. The editorial support regarding the status of the article process was excellent, and they informed me every day until the acceptance of the current status of the article version, and regarding how to answer questions, the editorial support was excellent, timely, and friendly, and they answered questions as soon as possible and did not hesitate. The quality of the journal was excellent and it made me proud to be acquainted with the journal, and I sincerely look forward to extensive scientific collaborations in any field. I hope for increasing success and pride for the International Journal of Social Science Research and Review and all scientific and knowledge-based communities. Thank you

img

Bhuvanagiri Sathya Sindhuja

"I would like to express my sincere appreciation for the opportunity to contribute to this esteemed journal. The publication process was smooth, well-coordinated, and the peer reviewers deemed highly professional. The editorial team demonstrated exceptional diligence and support at every stage, ensuring a seamless experience from submission to final publication. I am truly honored to be featured in such a reputable platform and look forward to future collaborations."

img

Safana Abdullah Algutaini

Testimonial for the Journal of Biomedical Research and Clinical Advancements It was a truly rewarding experience publishing our study, "Single-Surgeon Outcomes of Left Ventricular Aneurysm Repair in Wartime Syria: A 10-Year Retrospective Study at Damascus University Cardiac Surgery Hospital," with the Journal of Biomedical Research and Clinical Advancements. The editorial and peer-review process was both rigorous and efficient, demonstrating a high standard of academic integrity and scientific scrutiny. The journal’s commitment to open access and global health equity is evident in its support of research emerging from conflict-affected and resource-limited settings—making our work not only visible but impactful. The professionalism of the editorial team, the speed of communication, and the clarity of submission guidelines all contributed to a smooth publication process. We were particularly impressed by the quality of the publication layout and the prompt indexing of our article, which enhances its accessibility to clinicians, researchers, and policymakers worldwide. We are proud to have contributed to this journal and highly recommend it to fellow researchers seeking a reputable platform to disseminate clinically significant and globally relevant findings.