Dresden 2026 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 22: Pattern Formation
DY 22.3: Vortrag
Dienstag, 10. März 2026, 10:00–10:15, ZEU/0118
Pattern formation and route to chaos in a two-species reaction-diffusion model with one conservation law — •Simon Navia Rafide1 and Uwe Thiele2 — 1University of Münster, Münster Germany — 2University of Münster, Münster Germany
In many intracellular reactions, the total amount of a substance remains constant. For example, in reactions involving proteins that can adopt different conformations, it is possible to observe spatio-temporal concentration patterns that differ in their behaviour from those in systems without such constraints. We explore a relatively simple two-species reaction-diffusion model with a single mass conservation law governing cell polarisation [1, 2]. Here, we investigate the bifurcation behaviour of the model in detail and, using numerical continuation and time simulations, show that time-periodic patterns follow a period-doubling route to chaos, which appear in two different flavours. Moreover, we propose an approximate model based on the first two instability modes that allows us to understand the underlying mechanisms behind the first steps of pattern formation.
[1] Kuwamura, M., Izuhara, H., & Ei, S. I., Oscillations and bifurcation structure of reaction-diffusion model for cell polarity formation. J. Math. Biol., 84, 2022. [2] S. Ishihara, M. Otsuji, A. Mochizuki, Transient and steady state of massconserved reaction-diffusion systems, Phys. Rev. E 75, 015203, 2007.
Keywords: Chaos; Spatiotemporal patterns; Bifurcations; extended systems; Conservation laws