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 …
