Bifurcation structure in mathematical neuron models

Speaker: Prof. Roberto Barrio
Affiliation: Computational Dynamics Group, University of Zaragoza, Zaragoza, Spain

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Bursting phenomena are found in a wide variety of fast–slow systems. In this talk, I  present a global analysis of the main elements, focusing on the homoclinic bifurcations, involved in the bursting dynamics, exemplified in the Hindmarsh–Rose neuron model. Working in a three-parameter space, the results of our numerical analysis show a complex atlas of bifurcations, which extends from the singular limit to regions where a fast–slow perspective no longer applies. Based on this information, we propose a global theoretical description that includes surfaces of codimension-one homoclinic bifurcations that are exponentially close to each other, islands of homoclinic bifurcations, etc. These curves organize the bifurcations associated with the spike-adding process common in most mathematical neuron models. This talk is based on the recent publications: “Homoclinic organization in the Hindmarsh–Rose model: A three parameter study”, R Barrio, S Ibañez, L Perez, Chaos 30 (5), 053132, 2020 and “Spike-adding structure in fold/hom bursters”, R Barrio, S Ibañez, L Perez, S Serrano, Communications in Nonlinear Science and Numerical Simulation 83, 105100, 2020.   

Seminar language: English

Chairman: Jacek Gapiński

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