Spatial clustering of interacting bugs: Lévy flights versus Gaussian jumps

A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption that the reproduction rate depends on the crowding in the neigh...

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Bibliographic Details
Published in:Europhysics letters 2010-11, Vol.92 (4), p.40011
Main Authors: Heinsalu, E, Hernández-García, E, López, C
Format: Article
Language:English
Subjects:
02.50.Ey
05.40.-a
05.40.Fb
Competition
Crowding
Diffusion
Dynamical systems
Dynamics
Gaussian
Reproduction
Two dimensional
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Summary:A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption that the reproduction rate depends on the crowding in the neighborhood. The spatial dynamics corresponds either to normal diffusion characterized by Gaussian jumps or to superdiffusion characterized by Lévy flights. It is observed that in both cases periodic patterns occur for appropriate parameters of the model, indicating that the general macroscopic collective behavior of the system is more strongly influenced by the competition for the resources than by the type of spatial dynamics. However, some differences arise that are discussed.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/92/40011