| Title: | An aggregation model of cockroaches with fast-or-slow motion dichotomy |
| Author(s): | Elias J; Izuhara H; Mimura M; Tang BQ; |
| Address: | "Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010, Graz, Austria. Faculty of Engineering, University of Miyazaki, 1-1 Gakuen Kibanadai Nishi, Miyazaki, 889-2192, Japan. izuhara@cc.miyazaki-u.ac.jp. Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima City, Hiroshima, 739-8526, Japan" |
| DOI: | 10.1007/s00285-022-01797-1 |
| ISSN/ISBN: | 1432-1416 (Electronic) 0303-6812 (Linking) |
| Abstract: | "We propose a mathematical model, namely a reaction-diffusion system, to describe social behaviour of cockroaches. An essential new aspect in our model is that the dispersion behaviour due to overcrowding effect is taken into account as a counterpart to commonly studied aggregation. This consideration leads to an intriguing new phenomenon which has not been observed in the literature. Namely, due to the competition between aggregation towards areas of higher concentration of pheromone and dispersion avoiding overcrowded areas, the cockroaches aggregate more at the transition area of pheromone. Moreover, we also consider the fast reaction limit where the switching rate between active and inactive subpopulations tends to infinity. By utilising improved duality and energy methods, together with the regularisation of heat operator, we prove that the weak solution of the reaction-diffusion system converges to that of a reaction-cross-diffusion system" |
| Keywords: | "Animals *Cockroaches Diffusion Models, Theoretical Pheromones Social Behavior Aggregation versus dispersion Fast reaction limit German cockroach Improved duality method Reaction-diffusion equations;" |
| Notes: | "MedlineElias, Jan Izuhara, Hirofumi Mimura, Masayasu Tang, Bao Q eng Research Support, Non-U.S. Gov't Germany 2022/09/14 J Math Biol. 2022 Sep 13; 85(3):28. doi: 10.1007/s00285-022-01797-1" |
