In May, Professor of Mathematics Stanislav Mintchev co-organized a minisymposium at the 2023 Society for Industrial and Applied Mathematics (SIAM) Conference on Applications of Dynamical Systems (DS23) in Portland, Oregon. 

The primary objective of DS23 is to curate a balanced compilation of application-oriented content intertwined with the mathematical foundations that underpin and bolster the discipline. The conference aims to foster a cross-pollination of ideas across various application areas and facilitate enhanced communication among developers of dynamical systems techniques, as well as mathematicians, scientists, and engineers who leverage these techniques in their work.

The minisymposium, titled "Oscillation Propagation in Continuous and Discrete-Space Reaction-Diffusion Type Networks," was divided into two parts and comprised a series of presentations.

During Part 1 of the minisymposium, Professor Mintchev shared the outcomes of his collaboration with Benjamin Ambrosio from Le Havre Normandie University, France. In Part 2, the session was jointly presented with Cooper Adjunct Professor Brian Frost-Laplante EE'19. 

ABSTRACT
Mathematical techniques are critical to the understanding of brain wave measurements. Examples include applications to recordings from the macaque visual cortex, visual navigation models for the Drosophila, and wave recordings via EEG at the whole-brain scale. The seminal work of Hodgkin and Huxley (HH) in the 1950’s introduced an area of mathematical neuroscience focused on signal processing and transmission throughout the nervous system. Reaction-diffusion systems such as the original HH PDE provide a rich and successful platform for addressing such questions.

In the 1960’s, FitzHugh’s work provided a simplified model that nevertheless features both local oscillation and excitatory dynamics. Stemming from the original Hodgkin-Huxley model, a PDE extension of the FitzHugh-Nagumo model has been used in a variety of investigations seeking to understand how excitable tissues respond to and propagate current stimulation. Such models combine a standard mechanism for spatial diffusion via a Laplacian term, with a substantial time-nonlinearity that features timescale separation and related consequences.

Many models of mathematical neuroscience fall generally under the category of reaction-diffusion networks. In order to gain perspective on future directions for this line of work, this minisymposium seeks to bring together applied mathematicians that have contributed recently to the field by way of the implementation of such models and their analysis.