{"id":{"repo_id":"exeter","oai_identifier":"oai:figshare.com:article/32605302"},"canonical_url":"https://search.dev.ndltd.org/etd/exeter/oai:figshare.com:article/32605302","repository":{"repo_id":"exeter","name":"University of Exeter","base_url":"https://api.figshare.com/v2/oai"},"display":{"title":"Dynamical Systems Analysis of Neural Circuits with Applications to Physiological Processes","abstract":"Reproductive function in mammals is regulated by the pulsatile secretion of gonadotropin releasing hormone (GnRH), controlled by a hypothalamic neuronal oscillator known as the GnRH pulse generator. The timing and pattern of GnRH secretion are essential, with disruptions leading to reproductive dysfunction. Reproduction is fundamentally controlled by the brain, with the GnRH pulse generator acting as an integrative hub that receives modulatory inputs from various brain regions. These inputs dynamically shape GnRH activity in response to internal and external stimuli. However, the neuronal mechanisms underlying the modulation and disruption of GnRH pulsatility remain poorly understood, representing a central problem in reproductive neuroendocrinology. Using mathematical modelling, this thesis investigates the dynamical mechanisms underlying neuronal network activity, motivated by the role of the posterodorsal medial amygdala (MePD) as a key modulatory input to the GnRH pulse generator. We develop a biologically informed model of the MePD circuit to examine the role of interactions between glutamatergic and GABAergic neuronal populations in shaping circuit dynamics. The model reveals how external input and intrinsic excitatory–inhibitory balance control the emergence of oscillatory activity in the circuit and shape the MePD output that acts downstream of the GnRH pulse generator. In contrast to earlier assumptions of constant MePD output, the model establishes the plausibility of oscillatory dynamics and predicts a non-monotonic influence of glutamatergic MePD projections on the GnRH pulse generator, supported by in vivo experiments. Analysis of the MePD model indicates that the emergence of oscillatory dynamics can occur via a non-canonical global bifurcation: a heteroclinic loop connecting a nonhyperbolic saddle-node and a hyperbolic saddle equilibrium. Motivated by the finding of this geometric structure, we introduce and analyse a novel global bifurcation mechanism, termed the non-central SNICeroclinic, which provides a previously uncharacterised route to oscillations distinct from classical scenarios, involving Hopf, homoclinic, or saddle-node on invariant circle (SNIC) bifurcations. We analyse the unfolding of the non-central SNICeroclinic bifurcation in a minimal-dimension (planar) case where the non-hyperbolic point is assumed to undergo a saddle-node bifurcation. Building on this framework, we identify a further bifurcation involving a heteroclinic loop between two saddle-nodes, which we term the SNIC². We show that SNIC² acts as an organising centre governing transitions between quiescent, oscillatory, bistable, and up-and-down state dynamics. Importantly, we demonstrate that SNIC² arises across multiple phenomenological mean-field neuronal models, including Wilson–Cowan (that MePD circuit model is based on), Tsodyks–Markram, and Jansen–Rit formulations, indicating that it represents a common organising geometry underlying state transitions driven by changes in excitation–inhibition balance, independent of specific model details. The dynamical systems mechanisms characterised here (SNICeroclinic and SNIC²) provide a framework for understanding how perturbations to neuronal circuits induce qualitative changes in activity. In terms of the MePD circuit, this framework helps explain how targeted experimental perturbations may reshape activity patterns and influence the downstream GnRH pulse generator dynamics, and hence reproductive function. More broadly, this thesis establishes a unifying dynamical systems perspective on transitions between neuronal activity states, linking circuit-level mechanisms to functional modulation of neuronal dynamics.<p></p>","abstract_html":"Reproductive function in mammals is regulated by the pulsatile secretion of gonadotropin releasing hormone (GnRH), controlled by a hypothalamic neuronal oscillator known as the GnRH pulse generator. The timing and pattern of GnRH secretion are essential, with disruptions leading to reproductive dysfunction. Reproduction is fundamentally controlled by the brain, with the GnRH pulse generator acting as an integrative hub that receives modulatory inputs from various brain regions. These inputs dynamically shape GnRH activity in response to internal and external stimuli. However, the neuronal mechanisms underlying the modulation and disruption of GnRH pulsatility remain poorly understood, representing a central problem in reproductive neuroendocrinology. Using mathematical modelling, this thesis investigates the dynamical mechanisms underlying neuronal network activity, motivated by the role of the posterodorsal medial amygdala (MePD) as a key modulatory input to the GnRH pulse generator. We develop a biologically informed model of the MePD circuit to examine the role of interactions between glutamatergic and GABAergic neuronal populations in shaping circuit dynamics. The model reveals how external input and intrinsic excitatory–inhibitory balance control the emergence of oscillatory activity in the circuit and shape the MePD output that acts downstream of the GnRH pulse generator. In contrast to earlier assumptions of constant MePD output, the model establishes the plausibility of oscillatory dynamics and predicts a non-monotonic influence of glutamatergic MePD projections on the GnRH pulse generator, supported by in vivo experiments. Analysis of the MePD model indicates that the emergence of oscillatory dynamics can occur via a non-canonical global bifurcation: a heteroclinic loop connecting a nonhyperbolic saddle-node and a hyperbolic saddle equilibrium. Motivated by the finding of this geometric structure, we introduce and analyse a novel global bifurcation mechanism, termed the non-central SNICeroclinic, which provides a previously uncharacterised route to oscillations distinct from classical scenarios, involving Hopf, homoclinic, or saddle-node on invariant circle (SNIC) bifurcations. We analyse the unfolding of the non-central SNICeroclinic bifurcation in a minimal-dimension (planar) case where the non-hyperbolic point is assumed to undergo a saddle-node bifurcation. Building on this framework, we identify a further bifurcation involving a heteroclinic loop between two saddle-nodes, which we term the SNIC². We show that SNIC² acts as an organising centre governing transitions between quiescent, oscillatory, bistable, and up-and-down state dynamics. Importantly, we demonstrate that SNIC² arises across multiple phenomenological mean-field neuronal models, including Wilson–Cowan (that MePD circuit model is based on), Tsodyks–Markram, and Jansen–Rit formulations, indicating that it represents a common organising geometry underlying state transitions driven by changes in excitation–inhibition balance, independent of specific model details. The dynamical systems mechanisms characterised here (SNICeroclinic and SNIC²) provide a framework for understanding how perturbations to neuronal circuits induce qualitative changes in activity. In terms of the MePD circuit, this framework helps explain how targeted experimental perturbations may reshape activity patterns and influence the downstream GnRH pulse generator dynamics, and hence reproductive function. More broadly, this thesis establishes a unifying dynamical systems perspective on transitions between neuronal activity states, linking circuit-level mechanisms to functional modulation of neuronal dynamics.&lt;p&gt;&lt;/p&gt;","abstract_has_math":false,"creators":["Kate Nechyporenko (21049514)"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026-06-08T00:00:00Z","date_published":"2026-06-08T00:00:00Z","updated_at":"2026-07-27T19:32:43Z","subjects":["Dynamical Systems","Bifurcation Analysis","Reproduction","Amygdala"],"languages":[],"rights":["All rights reserved"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10779/exe.32605302.v1"],"render_values":[{"text":"10779/exe.32605302.v1","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Kate Nechyporenko (21049514)"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2026-06-08T00:00:00Z"]},{"key":"dc:relation","label":"Dc Relation","values":["https://figshare.com/articles/thesis/Dynamical_Systems_Analysis_of_Neural_Circuits_with_Applications_to_Physiological_Processes/32605302"]},{"key":"dc:type","label":"Dc Type","values":["Text","Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Dynamical Systems","Bifurcation Analysis","Reproduction","Amygdala"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["All rights reserved"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10779/exe.32605302.v1"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Reproductive function in mammals is regulated by the pulsatile secretion of gonadotropin releasing hormone (GnRH), controlled by a hypothalamic neuronal oscillator known as the GnRH pulse generator. The timing and pattern of GnRH secretion are essential, with disruptions leading to reproductive dysfunction. Reproduction is fundamentally controlled by the brain, with the GnRH pulse generator acting as an integrative hub that receives modulatory inputs from various brain regions. These inputs dynamically shape GnRH activity in response to internal and external stimuli. However, the neuronal mechanisms underlying the modulation and disruption of GnRH pulsatility remain poorly understood, representing a central problem in reproductive neuroendocrinology. Using mathematical modelling, this thesis investigates the dynamical mechanisms underlying neuronal network activity, motivated by the role of the posterodorsal medial amygdala (MePD) as a key modulatory input to the GnRH pulse generator. We develop a biologically informed model of the MePD circuit to examine the role of interactions between glutamatergic and GABAergic neuronal populations in shaping circuit dynamics. The model reveals how external input and intrinsic excitatory–inhibitory balance control the emergence of oscillatory activity in the circuit and shape the MePD output that acts downstream of the GnRH pulse generator. In contrast to earlier assumptions of constant MePD output, the model establishes the plausibility of oscillatory dynamics and predicts a non-monotonic influence of glutamatergic MePD projections on the GnRH pulse generator, supported by in vivo experiments. Analysis of the MePD model indicates that the emergence of oscillatory dynamics can occur via a non-canonical global bifurcation: a heteroclinic loop connecting a nonhyperbolic saddle-node and a hyperbolic saddle equilibrium. Motivated by the finding of this geometric structure, we introduce and analyse a novel global bifurcation mechanism, termed the non-central SNICeroclinic, which provides a previously uncharacterised route to oscillations distinct from classical scenarios, involving Hopf, homoclinic, or saddle-node on invariant circle (SNIC) bifurcations. We analyse the unfolding of the non-central SNICeroclinic bifurcation in a minimal-dimension (planar) case where the non-hyperbolic point is assumed to undergo a saddle-node bifurcation. Building on this framework, we identify a further bifurcation involving a heteroclinic loop between two saddle-nodes, which we term the SNIC². We show that SNIC² acts as an organising centre governing transitions between quiescent, oscillatory, bistable, and up-and-down state dynamics. Importantly, we demonstrate that SNIC² arises across multiple phenomenological mean-field neuronal models, including Wilson–Cowan (that MePD circuit model is based on), Tsodyks–Markram, and Jansen–Rit formulations, indicating that it represents a common organising geometry underlying state transitions driven by changes in excitation–inhibition balance, independent of specific model details. The dynamical systems mechanisms characterised here (SNICeroclinic and SNIC²) provide a framework for understanding how perturbations to neuronal circuits induce qualitative changes in activity. In terms of the MePD circuit, this framework helps explain how targeted experimental perturbations may reshape activity patterns and influence the downstream GnRH pulse generator dynamics, and hence reproductive function. More broadly, this thesis establishes a unifying dynamical systems perspective on transitions between neuronal activity states, linking circuit-level mechanisms to functional modulation of neuronal dynamics.<p></p>"]},{"key":"dc:title","label":"Title","values":["Dynamical Systems Analysis of Neural Circuits with Applications to Physiological Processes"]}]}],"canonical_facts":{"dc:creator":["Kate Nechyporenko (21049514)"],"dc:date":["2026-06-08T00:00:00Z"],"dc:description":["Reproductive function in mammals is regulated by the pulsatile secretion of gonadotropin releasing hormone (GnRH), controlled by a hypothalamic neuronal oscillator known as the GnRH pulse generator. The timing and pattern of GnRH secretion are essential, with disruptions leading to reproductive dysfunction. Reproduction is fundamentally controlled by the brain, with the GnRH pulse generator acting as an integrative hub that receives modulatory inputs from various brain regions. These inputs dynamically shape GnRH activity in response to internal and external stimuli. However, the neuronal mechanisms underlying the modulation and disruption of GnRH pulsatility remain poorly understood, representing a central problem in reproductive neuroendocrinology. Using mathematical modelling, this thesis investigates the dynamical mechanisms underlying neuronal network activity, motivated by the role of the posterodorsal medial amygdala (MePD) as a key modulatory input to the GnRH pulse generator. We develop a biologically informed model of the MePD circuit to examine the role of interactions between glutamatergic and GABAergic neuronal populations in shaping circuit dynamics. The model reveals how external input and intrinsic excitatory–inhibitory balance control the emergence of oscillatory activity in the circuit and shape the MePD output that acts downstream of the GnRH pulse generator. In contrast to earlier assumptions of constant MePD output, the model establishes the plausibility of oscillatory dynamics and predicts a non-monotonic influence of glutamatergic MePD projections on the GnRH pulse generator, supported by in vivo experiments. Analysis of the MePD model indicates that the emergence of oscillatory dynamics can occur via a non-canonical global bifurcation: a heteroclinic loop connecting a nonhyperbolic saddle-node and a hyperbolic saddle equilibrium. Motivated by the finding of this geometric structure, we introduce and analyse a novel global bifurcation mechanism, termed the non-central SNICeroclinic, which provides a previously uncharacterised route to oscillations distinct from classical scenarios, involving Hopf, homoclinic, or saddle-node on invariant circle (SNIC) bifurcations. We analyse the unfolding of the non-central SNICeroclinic bifurcation in a minimal-dimension (planar) case where the non-hyperbolic point is assumed to undergo a saddle-node bifurcation. Building on this framework, we identify a further bifurcation involving a heteroclinic loop between two saddle-nodes, which we term the SNIC². We show that SNIC² acts as an organising centre governing transitions between quiescent, oscillatory, bistable, and up-and-down state dynamics. Importantly, we demonstrate that SNIC² arises across multiple phenomenological mean-field neuronal models, including Wilson–Cowan (that MePD circuit model is based on), Tsodyks–Markram, and Jansen–Rit formulations, indicating that it represents a common organising geometry underlying state transitions driven by changes in excitation–inhibition balance, independent of specific model details. The dynamical systems mechanisms characterised here (SNICeroclinic and SNIC²) provide a framework for understanding how perturbations to neuronal circuits induce qualitative changes in activity. In terms of the MePD circuit, this framework helps explain how targeted experimental perturbations may reshape activity patterns and influence the downstream GnRH pulse generator dynamics, and hence reproductive function. More broadly, this thesis establishes a unifying dynamical systems perspective on transitions between neuronal activity states, linking circuit-level mechanisms to functional modulation of neuronal dynamics.<p></p>"],"dc:identifier":["10779/exe.32605302.v1"],"dc:relation":["https://figshare.com/articles/thesis/Dynamical_Systems_Analysis_of_Neural_Circuits_with_Applications_to_Physiological_Processes/32605302"],"dc:rights":["All rights reserved"],"dc:subject":["Dynamical Systems","Bifurcation Analysis","Reproduction","Amygdala"],"dc:title":["Dynamical Systems Analysis of Neural Circuits with Applications to Physiological Processes"],"dc:type":["Text","Thesis"]},"updated_at":"2026-07-27T19:32:43Z"}