Title: Heteroclinic cycles under forced symmetry breaking: coupled oscillators, reduced dynamics, normal forms and invariant manifolds Abstract: Networks of oscillatory units are an active area of research due to their connections with brain functions and the complex collective dynamic arising on these models. We …
Title: Rare chaos in neural models Abstract: We discuss a number of examples illustrating the onset of complex chaotic dynamics in slow-fast models of individual neurons. These, underlying transition between activity types, include torus breakdown, various homoclinic bifurcations of periodic orbits and equilibria, geometries of the …
Title: Geometric singular perturbation analysis of the multiple-timescale Hodgkin-Huxley equations Abstract: The Hodgkin-Huxley (HH) equations [1] are one of the most successful models to describe the propagation of action potentials in neurons. For their work, Hodgkin and Huxley received the 1963 Nobel Prize in Physiology and …
Title: Neuron scale modeling of prion production with the Unfolded Protein Response Abstract: After reminding a brief biological context, we develop a mathematical model that describes concentration dynamics of PrPC and PrPSc prion proteins at the neuron scale and includes the effect of the …
Title: Multiple time-scale dynamics in neural mass models: canard solutions and critical regimes Abstract: Epileptic seizures are very often hallmarked by pre-ictal phases which constitute a possible window of opportunity to trigger electrical stimulation with the objective to prevent seizure initiation. In …
Title: Controlling seizure propagation in large-scale brain networks Abstract: Information transmission in the human brain is a fundamentally dynamic network process. In partial epilepsy, this process is perturbed and highly synchronous seizures originate in a local network, the so-called epileptogenic zone (EZ), before recruiting other …
Title: Saga of making swim CPG models Abstract: This talk will focus on a derivation of accurate math models for rhythm-generating neural circuits that control swim behaviors in specific sea slugs. January 29th, …
Title: Neuromechanics of working memory errors: a neural field approach Abstract: We develop and analyze neurocomputational models to account for systematic errors in visual working memory tasks. Our framework is a neural field model with lateral …
Title: Role of gap junctions in a neuron astrocyte network model Abstract: A detailed biophysical model for a neuron/astrocyte network is developed in order to explore mechanisms responsible for the initiation and propagation of cortical spreading depolarizations and the …
Title: Emergence of vascularization networks Abstract: Networks are patterns created dynamically in order to optimize the distribution or the exchange of quantities in an environment. They appear naturally in Nature, for instance in human biology (neural network, respiratory …
