# Competition of Species with Intra-Specific Competition

N. Apreutesei; A. Ducrot; V. Volpert

Mathematical Modelling of Natural Phenomena (2008)

- Volume: 3, Issue: 4, page 1-27
- ISSN: 0973-5348

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topApreutesei, 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 -

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