Committee Chair
Kong, Lingju
Committee Member
Wang, Xiunan; Wang, Jin; Graef, John R.
College
College of Arts and Sciences
Publisher
University of Tennessee at Chattanooga
Place of Publication
Chattanooga (Tenn.)
Abstract
We introduce a compartmental differential equation model to study the dynamics of user adoption and abandonment for a single product. The model integrates two forms of abandonment: infectious, driven by user interactions, and non-infectious, prompted by external influences. Notably, the infectious abandonment coefficient varies linearly with the number of previous users. We investigate the existence of equilibria of the model and derive the threshold quantity ℛ0. The user-free equilibrium is always present, and its stability is analyzed under the condition ℛ0 < 1. Moreover, a user-prevailing equilibrium does not exist when ℛ0 ≤ 1, but at least one user-prevailing equilibrium is guaranteed when ℛ0 > 1. We further characterize conditions for multiple equilibria and various bifurcations, including saddle-node, 𝑆-shaped, and Hopf bifurcations, and formulate an optimal control problem. Numerical simulations validate our theoretical findings, and the historical LinkedIn and YouTube data calibrate the model to forecast future user adoption trends.
Acknowledgments
I would like to extend my heartfelt gratitude to my advisor, Dr. Lingju Kong, for his support, guidance, and encouragement. His patience, feedback, and enthusiasm for research have been truly inspiring. I sincerely appreciate the time and effort he has invested in mentoring me, and I could not have asked for a more supportive advisor. I express my appreciation to all the professors who taught me during my time in the program. Their engaging lectures have helped me strengthen my background in the f ield. I appreciate Dr. Xiunan Wang, Dr. Jin Wang, and Dr. John Graef for their contributions as members of my committee. I am grateful to Dr. Christopher L. Cox, Ms. Deborah Barr, Dr. Francesco Barioli, and Dr. Lakmali Weerasena for their assistance and encouragement. I thank the Center of Excellence in Applied Computational Science and Engineering (CEACSE) for its financial support, which was instrumental in advancing this research.
Degree
M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.
Date
5-2025
Subject
Bifurcation theory; Consumer behavior--Mathematical models; Differential equations; Diffusion of innovations--Mathematical models; Nonlinear systems; Pontryagin spaces; Product life cycle--Mathematical models
Document Type
Masters theses
DCMI Type
Text
Extent
xiv, 49 leaves
Language
English
Rights
http://rightsstatements.org/vocab/InC/1.0/
License
http://creativecommons.org/licenses/by-nc-nd/3.0/
Date Available
11-30-2026
Recommended Citation
Nguyen, Uyen, "Modeling the dynamics of user adoption and abandonment for a single product" (2025). Masters Theses and Doctoral Dissertations.
https://scholar.utc.edu/theses/997
Revision
Department
Dept. of Mathematics