Competition of Species with Intra-Specific Competition

Apreutesei, N., Ducrot, A., and Volpert, V.. "Competition of Species with Intra-Specific Competition." Mathematical Modelling of Natural Phenomena 3.4 (2008): 1-27. <http://eudml.org/doc/222296>.

@article{Apreutesei2008,
abstract = { Intra-specific competition in population dynamics can be described by integro-differential equations where the integral term corresponds to nonlocal consumption of resources by individuals of the same population. Already the single integro-differential equation can show the emergence of nonhomogeneous in space stationary structures and can be used to model the process of speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom. 1 (2006), no. 1, 65-82], [S. Genieys et al., Comptes Rendus Biologies, 329 (11), 876-879 (2006)]. On the other hand, competition of two different species represents a well known and well studied model in population dynamics. In this work we study how the intra-specific competition can influence the competition between species. We will prove the existence of travelling waves for the case where the support of the kernel of the integral is sufficiently narrow. Numerical simulations will be carried out in the case of large supports. },
author = {Apreutesei, N., Ducrot, A., Volpert, V.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {integro-differential equation; Fredholm property; travelling waves},
language = {eng},
month = {12},
number = {4},
pages = {1-27},
publisher = {EDP Sciences},
title = {Competition of Species with Intra-Specific Competition},
url = {http://eudml.org/doc/222296},
volume = {3},
year = {2008},
}

TY - JOUR
AU - Apreutesei, N.
AU - Ducrot, A.
AU - Volpert, V.
TI - Competition of Species with Intra-Specific Competition
JO - Mathematical Modelling of Natural Phenomena
DA - 2008/12//
PB - EDP Sciences
VL - 3
IS - 4
SP - 1
EP - 27
AB - Intra-specific competition in population dynamics can be described by integro-differential equations where the integral term corresponds to nonlocal consumption of resources by individuals of the same population. Already the single integro-differential equation can show the emergence of nonhomogeneous in space stationary structures and can be used to model the process of speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom. 1 (2006), no. 1, 65-82], [S. Genieys et al., Comptes Rendus Biologies, 329 (11), 876-879 (2006)]. On the other hand, competition of two different species represents a well known and well studied model in population dynamics. In this work we study how the intra-specific competition can influence the competition between species. We will prove the existence of travelling waves for the case where the support of the kernel of the integral is sufficiently narrow. Numerical simulations will be carried out in the case of large supports.
LA - eng
KW - integro-differential equation; Fredholm property; travelling waves
UR - http://eudml.org/doc/222296
ER -