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Saddle-Node Separatrix-Loops and Neuronal Network Dynamics

Krasimira Tsaneva-Atanasova, University of Exeter
Tuesday October 29, 12-1pm
Zoom Link:听
In Person: 550 Sherbrooke, Room 189

Abstract:听Normal reproductive function and fertility rely on the rhythmic release of gonadotropin- releasing hormone (GnRH), orchestrated by the hypothalamic GnRH pulse generator. The posterodorsal subnucleus of the medial amygdala (MePD), a brain region implicated in pro- cessing external environmental cues including stress effects, acts as a key regulator of the GnRH pulse generator. However, the specific neuronal pathways governing the dynamic, stress-induced modulation of GnRH secretion remain largely elusive. Here we employ computational modelling and analysis to investigate the effects of dynamic inputs on GnRH pulse generator activity.

To this end, we develop and analyse a mathematical model representing MePD neuronal circuits comprised of GABAergic and glutamatergic neuronal populations, integrating it with our GnRH pulse generator model. Numerical bifurcation analysis enables us to identify critical model parameters and distinct neuronal network dynamic regimes. Moreover, our analysis highlights the significance of saddle-node separatrix-loops in influencing these dynamics. To investigate further the saddle-node separatrix-loops identified in our model, we propose unfolding a generic heteroclinic loop featuring one nonhyperbolic and one hyperbolic saddle using discrete (Poincar茅) maps.