Spatial clustering of interacting bugs: Lévy flights versus Gaussian jumps
IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB) - E-07122 Palma de Mallorca, Spain
2 National Institute of Chemical Physics and Biophysics - Rävala 10, Tallinn 15042, Estonia
Accepted: 5 November 2010
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.
PACS: 02.50.Ey – Stochastic processes / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.40.Fb – Random walks and Levy flights
© EPLA, 2010