Puberty has remained a longstanding biological puzzle for scientists. Much remains to be understood about mechanisms that trigger this important development. What is however established is that, the activity of a certain network of neurons called Gonadotropin-Releasing Hormone (GnRH) neurons lies at the very heart of this puzzle. For my thesis, I develop and analyze a deterministic mathematical model of a GnRH neuron consisting of a system of differential equations based on experimental observations and published results. Using the results of the model we test hypotheses of possible neurobiological mechanisms mediating the transitions in the activity patterns of GnRH neurons across puberty.
For a regime of parameter values the model neuron exhibits subthreshold (small-amplitude) membrane oscillations in conjunction with spikes (large-amplitude oscillations). Their intermixing can produce complicated patterns called mixed mode oscillations (MMOs). Mathematically, the occurrence of MMOs raises important questions pertaining to the geometry of invariant manifolds of the underlying dynamical system. Using geometric singular perturbation theory methods and mathematical software packages I analyze the MMOs arising in the GnRH model. This analysis is presented through a sequence of theorems that comprise the core results of my thesis.
","abstract_html":"<p>Puberty has remained a longstanding biological puzzle for scientists. Much remains to be understood about mechanisms that trigger this important development. What is however established is that, the activity of a certain network of neurons called Gonadotropin-Releasing Hormone (GnRH) neurons lies at the very heart of this puzzle. For my thesis, I develop and analyze a deterministic mathematical model of a GnRH neuron consisting of a system of differential equations based on experimental observations and published results. Using the results of the model we test hypotheses of possible neurobiological mechanisms mediating the transitions in the activity patterns of GnRH neurons across puberty.</p><p>For a regime of parameter values the model neuron exhibits subthreshold (small-amplitude) membrane oscillations in conjunction with spikes (large-amplitude oscillations). Their intermixing can produce complicated patterns called mixed mode oscillations (MMOs). Mathematically, the occurrence of MMOs raises important questions pertaining to the geometry of invariant manifolds of the underlying dynamical system. Using geometric singular perturbation theory methods and mathematical software packages I analyze the MMOs arising in the GnRH model. This analysis is presented through a sequence of theorems that comprise the core results of my thesis.</p>","abstract_has_math":false,"creators":["Banerjee, Sayanti P."],"institution":"The Ohio State University","degree_name":"Doctor of Philosophy","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Best, Janet"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-05-21","date_published":"2013-05-21","updated_at":"2026-07-24T03:36:08Z","subjects":["Biology","Mathematics","Neurosciences","GnRH neurons","Puberty","Mathematical Model","Mixed Mode Oscillations"],"languages":["English"],"rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://rave.ohiolink.edu/etdc/view?acc_num=osu1357249691","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Best, Janet"]},{"key":"dc:creator","label":"Author","values":["Banerjee, Sayanti P."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-05-21"]},{"key":"dc:publisher","label":"Institution","values":["The Ohio State University / OhioLINK"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The Ohio State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Biology","Mathematics","Neurosciences","GnRH neurons","Puberty","Mathematical Model","Mixed Mode Oscillations"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://rave.ohiolink.edu/etdc/view?acc_num=osu1357249691"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Puberty has remained a longstanding biological puzzle for scientists. Much remains to be understood about mechanisms that trigger this important development. What is however established is that, the activity of a certain network of neurons called Gonadotropin-Releasing Hormone (GnRH) neurons lies at the very heart of this puzzle. For my thesis, I develop and analyze a deterministic mathematical model of a GnRH neuron consisting of a system of differential equations based on experimental observations and published results. Using the results of the model we test hypotheses of possible neurobiological mechanisms mediating the transitions in the activity patterns of GnRH neurons across puberty.
For a regime of parameter values the model neuron exhibits subthreshold (small-amplitude) membrane oscillations in conjunction with spikes (large-amplitude oscillations). Their intermixing can produce complicated patterns called mixed mode oscillations (MMOs). Mathematically, the occurrence of MMOs raises important questions pertaining to the geometry of invariant manifolds of the underlying dynamical system. Using geometric singular perturbation theory methods and mathematical software packages I analyze the MMOs arising in the GnRH model. This analysis is presented through a sequence of theorems that comprise the core results of my thesis.
"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf","p.179","13.73 MB"]},{"key":"dc:title","label":"Title","values":["A Mathematical Model for the Transition in Firing Patterns Across Puberty of a Gonadotropin-Releasing Hormone Neuron"]}]}],"canonical_facts":{"dc:contributor":["Best, Janet"],"dc:creator":["Banerjee, Sayanti P."],"dc:date":["2013-05-21"],"dc:description":["Puberty has remained a longstanding biological puzzle for scientists. Much remains to be understood about mechanisms that trigger this important development. What is however established is that, the activity of a certain network of neurons called Gonadotropin-Releasing Hormone (GnRH) neurons lies at the very heart of this puzzle. For my thesis, I develop and analyze a deterministic mathematical model of a GnRH neuron consisting of a system of differential equations based on experimental observations and published results. Using the results of the model we test hypotheses of possible neurobiological mechanisms mediating the transitions in the activity patterns of GnRH neurons across puberty.
For a regime of parameter values the model neuron exhibits subthreshold (small-amplitude) membrane oscillations in conjunction with spikes (large-amplitude oscillations). Their intermixing can produce complicated patterns called mixed mode oscillations (MMOs). Mathematically, the occurrence of MMOs raises important questions pertaining to the geometry of invariant manifolds of the underlying dynamical system. Using geometric singular perturbation theory methods and mathematical software packages I analyze the MMOs arising in the GnRH model. This analysis is presented through a sequence of theorems that comprise the core results of my thesis.
"],"dc:format":["application/pdf","p.179","13.73 MB"],"dc:identifier":["http://rave.ohiolink.edu/etdc/view?acc_num=osu1357249691"],"dc:language":["English"],"dc:publisher":["The Ohio State University / OhioLINK"],"dc:rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."],"dc:subject":["Biology","Mathematics","Neurosciences","GnRH neurons","Puberty","Mathematical Model","Mixed Mode Oscillations"],"dc:title":["A Mathematical Model for the Transition in Firing Patterns Across Puberty of a Gonadotropin-Releasing Hormone Neuron"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Ohio State University"]},"updated_at":"2026-07-24T03:36:08Z"}