Competition of Species with Intra-Specific Competition
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 4, pp. 1-27
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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.
@article{10_1051_mmnp:2008068,
author = {N. Apreutesei and A. Ducrot and V. Volpert},
title = {Competition of {Species} with {Intra-Specific} {Competition}},
journal = {Mathematical modelling of natural phenomena},
pages = {1--27},
publisher = {mathdoc},
volume = {3},
number = {4},
year = {2008},
doi = {10.1051/mmnp:2008068},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008068/}
}
TY - JOUR AU - N. Apreutesei AU - A. Ducrot AU - V. Volpert TI - Competition of Species with Intra-Specific Competition JO - Mathematical modelling of natural phenomena PY - 2008 SP - 1 EP - 27 VL - 3 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008068/ DO - 10.1051/mmnp:2008068 LA - en ID - 10_1051_mmnp:2008068 ER -
%0 Journal Article %A N. Apreutesei %A A. Ducrot %A V. Volpert %T Competition of Species with Intra-Specific Competition %J Mathematical modelling of natural phenomena %D 2008 %P 1-27 %V 3 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008068/ %R 10.1051/mmnp:2008068 %G en %F 10_1051_mmnp:2008068
N. Apreutesei; A. Ducrot; V. Volpert. Competition of Species with Intra-Specific Competition. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 4, pp. 1-27. doi: 10.1051/mmnp:2008068
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