Dynamics of excitable cells: neurons and cardiomyocytes

Other Talks
Wednesday, May 10, 2023 - 11:00am for 1 hour (actually 50 minutes)
PLOS (second floor of Howey)
Roberto Barrio – Univ. of Zaragoza
Flavio Fenton
In recent years, much attention has been paid to the description of excitable media,
such as the dynamics of the brain and heart.
In both cases, the building blocks are excitable cells, neurons, and cardiomyocytes,
and a detailed look at the mathematics behind some of their mathematical models provides
a good starting point for answering some observed phenomena.
In this talk we show how some apparently  simple phenomena,
such as the spike-adding process,
have important consequences in the models and how various elements intervene behind their formation,
such as homoclinic bifurcations, fast-slow decompositions, "canards",
the completion of the Smale topological template, the formation of Morse surfaces
creating geometric bifurcations, etc.
Finally, we will illustrate its relevance in insect gait patterns and in the formation of cardiac arrhythmias.