Project Idea: Investigation of Traveling Waves in the Belousov-Zhabotinskii (BZ) Reaction, Jasmin Imran Alsous, Megan Matthews [Weinberg]

We are planning on looking at traveling wave solutions in the Belousov-Zhabotinskii (BZ) reaction, and in the Fitzhugh Nagumo (FHN) system. This will first include finding the traveling wave solutions in 1D, estimating the traveling wave velocities obtained for a traveling front and trigger waves, and determining the dispersion wave relation for a propagating pulse on a ring. This is interesting because there is a minimum size for the system below which propagating waves cannot be sustained on a periodic 1D domain (or a ring). This is of biological importance because it allows us to determine whether conditions such as fibrillations are possible for hearts of a certain size (e.g. humans can have fibrillations, but cats cannot). If time allows we plan to study these systems in 2D, by investigating the conditions that allow for spiral wave solutions. By studying these two systems, for which solutions are already known, we can become confident in our analysis of such coupled-PDE systems, and we hope/plan to use this knowledge in the analysis of our future research projects, such as examining the evolution of actin dynamics in migrating cells.

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