# Dynamics of Propagation Phenomena in Biological Pattern Formation

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 1, Issue: 1, page 98-119
- ISSN: 0973-5348

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topLiţcanu, 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 -

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