{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-2164"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-2164","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"Modeling the dynamics of user adoption and abandonment for a single product","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.","abstract_html":"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 &lt; 1. Moreover, a user-prevailing equilibrium does not exist when ℛ0 ≤ 1, but at least one user-prevailing equilibrium is guaranteed when ℛ0 &gt; 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.","abstract_has_math":false,"creators":["Nguyen, Uyen"],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Kong, Lingju","Wang, Xiunan; Wang, Jin; Graef, John R.","College of Arts and Sciences"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026-11-30T08:00:00Z","date_published":"2026-11-30T08:00:00Z","updated_at":"2026-07-24T05:47:21Z","subjects":["Bifurcation theory","Consumer behavior--Mathematical models","Differential equations","Diffusion of innovations--Mathematical models","Nonlinear systems","Pontryagin spaces","Product life cycle--Mathematical models"],"languages":["English","eng"],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/997","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kong, Lingju","Wang, Xiunan; Wang, Jin; Graef, John R.","College of Arts and Sciences"]},{"key":"dc:creator","label":"Author","values":["Nguyen, Uyen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-05-01T07:00:00Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-11-30T08:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Masters theses","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Bifurcation theory","Consumer behavior--Mathematical models","Differential equations","Diffusion of innovations--Mathematical models","Nonlinear systems","Pontryagin spaces","Product life cycle--Mathematical models"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/997"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Mathematics","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."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Modeling the dynamics of user adoption and abandonment for a single product"]}]}],"canonical_facts":{"dc:contributor":["Kong, Lingju","Wang, Xiunan; Wang, Jin; Graef, John R.","College of Arts and Sciences"],"dc:creator":["Nguyen, Uyen"],"dc:date":["2025-05-01T07:00:00Z"],"dc:date.available":["2026-11-30T08:00:00Z"],"dc:description":["Dept. of Mathematics","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."],"dc:description.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."],"dc:identifier":["https://scholar.utc.edu/theses/997"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Bifurcation theory","Consumer behavior--Mathematical models","Differential equations","Diffusion of innovations--Mathematical models","Nonlinear systems","Pontryagin spaces","Product life cycle--Mathematical models"],"dc:title":["Modeling the dynamics of user adoption and abandonment for a single product"],"dc:type":["Masters theses","Text"]},"updated_at":"2026-07-24T05:47:21Z"}