Dynamics of Propagation Phenomena in Biological Pattern Formation

Liţcanu, G., and Velázquez, J. J.L.. "Dynamics of Propagation Phenomena in Biological Pattern Formation." Mathematical Modelling of Natural Phenomena 1.1 (2010): 98-119. <http://eudml.org/doc/222350>.

@article{Liţcanu2010,
abstract = { A large variety of complex spatio-temporal patterns emerge from the processes occurring in biological systems, one of them being the result of propagating phenomena. This wave-like structures can be modelled via reaction-diffusion equations. If a solution of a reaction-diffusion equation represents a travelling wave, the shape of the solution will be the same at all time and the speed of propagation of this shape will be a constant. Travelling wave solutions of reaction-diffusion systems have been extensively studied by several authors from experimental, numerical and analytical points-of-view. In this paper we focus on two reaction-diffusion models for the dynamics of the travelling waves appearing during the process of the cells aggregation. Using singular perturbation methods to study the structure of solutions, we can derive analytic formulae (like for the wave speed, for example) in terms of the different biochemical constants that appear in the models. The goal is to point out if the models can describe in quantitative manner the experimental observations. },
author = {Liţcanu, G., Velázquez, J. J.L.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {reaction-diffusion systems; travelling waves; singular perturbation methods},
language = {eng},
month = {3},
number = {1},
pages = {98-119},
publisher = {EDP Sciences},
title = {Dynamics of Propagation Phenomena in Biological Pattern Formation},
url = {http://eudml.org/doc/222350},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Liţcanu, G.
AU - Velázquez, J. J.L.
TI - Dynamics of Propagation Phenomena in Biological Pattern Formation
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 1
IS - 1
SP - 98
EP - 119
AB - A large variety of complex spatio-temporal patterns emerge from the processes occurring in biological systems, one of them being the result of propagating phenomena. This wave-like structures can be modelled via reaction-diffusion equations. If a solution of a reaction-diffusion equation represents a travelling wave, the shape of the solution will be the same at all time and the speed of propagation of this shape will be a constant. Travelling wave solutions of reaction-diffusion systems have been extensively studied by several authors from experimental, numerical and analytical points-of-view. In this paper we focus on two reaction-diffusion models for the dynamics of the travelling waves appearing during the process of the cells aggregation. Using singular perturbation methods to study the structure of solutions, we can derive analytic formulae (like for the wave speed, for example) in terms of the different biochemical constants that appear in the models. The goal is to point out if the models can describe in quantitative manner the experimental observations.
LA - eng
KW - reaction-diffusion systems; travelling waves; singular perturbation methods
UR - http://eudml.org/doc/222350
ER -