Spatial patterns of competing random walkers

@article{HernndezGarca2015SpatialPO,
  title={Spatial patterns of competing random walkers},
  author={Emilio Hern{\'a}ndez‐Garc{\'i}a and E. Heinsalu and Crist{\'o}bal L{\'o}pez},
  journal={Ecological Complexity},
  year={2015},
  volume={21},
  pages={166-176}
}

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References

SHOWING 1-10 OF 71 REFERENCES
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
Clustering determines who survives for competing Brownian and Lévy walkers.
TLDR
It is observed that no influence of the type of motion occurs when the two species are in a well-mixed unstructured state, but as soon as the species develop spatial clustering, the one forming more concentrated clusters gets a competitive advantage and eliminates the other.
Competitive Brownian and Lévy walkers.
TLDR
By dividing initially everyone into different families and following their descent it is possible to show that mixing of families and their competition is greatly influenced by the spatial dynamics, so that spatial configurations under the two types of diffusion become more similar.
Reproductive pair correlations and the clustering of organisms
TLDR
It is shown that a population of independent, random-walking organisms (‘brownian bugs’), reproducing by binary division and dying at constant rates, spontaneously aggregates.
Clustering, advection, and patterns in a model of population dynamics with neighborhood-dependent rates.
TLDR
A simple model of population dynamics which considers reproducing individuals or particles with birth and death rates depending on the number of other individuals in their neighborhood, and derives the equation for the macroscopic density of particles, performs a linear stability analysis, and shows that there is a finite-wavelength instability leading to pattern formation.
Demographic fluctuations in a population of anomalously diffusing individuals.
  • P. Olla
  • Economics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
TLDR
The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically and the growth rate of the fluctuations becomes independent of the Hurst exponent of the CTRW.
Clumped Distribution by Neighbourhood Competition
Abstract The paper studies the spatial distribution of individuals competing for a continuously distributed resource in one-dimensional space. An individual diffuses randomly, and is assumed to
Selective advantage of diffusing faster.
TLDR
It is shown that even a relative difference in diffusivity on the order of a few percent may lead to a strong bias in the coarsening process favoring the more agile species.
Spatial patterns in non-locally interacting particle systems
Abstract.The influence of spatially non-local interactions on the aggregation, competition, and growth dynamics of interacting particle systems has been recently addressed. In this paper we survey
...
...