Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources

S. Genieys; V. Volpert; P. Auger

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 1, Issue: 1, page 63-80
  • ISSN: 0973-5348

Abstract

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We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.

How to cite

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Genieys, S., Volpert, V., and Auger, P.. "Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources." Mathematical Modelling of Natural Phenomena 1.1 (2010): 63-80. <http://eudml.org/doc/222210>.

@article{Genieys2010,
abstract = { We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed. },
author = {Genieys, S., Volpert, V., Auger, P.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {integro-differential equations; patterns and waves; evolution},
language = {eng},
month = {3},
number = {1},
pages = {63-80},
publisher = {EDP Sciences},
title = {Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources},
url = {http://eudml.org/doc/222210},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Genieys, S.
AU - Volpert, V.
AU - Auger, P.
TI - Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 1
IS - 1
SP - 63
EP - 80
AB - We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.
LA - eng
KW - integro-differential equations; patterns and waves; evolution
UR - http://eudml.org/doc/222210
ER -

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