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Talks & Presentations

Nonlocally interacting particle systems: Lévy flights versus Gaussian jumps

By E. Heinsalu, E. Hernández-García, C. López
XVI Congreso de Física Estadística 2009

Interacting particle systems help us to model and to
understand various problems in fields as diverse as condensed
matter physics, chemical kinetics, population biology
(individual based models), or sociology (agent based
models).
A simple model that has been considered by several
authors in the context of population dynamics, in particular
in order to address plankton distribution and patchiness,
is the Brownian bug model. It consists of an
ensemble of Brownian particles, each one dying or reproducing
with given probabilities per unit of time. This
basic model lacks any interaction between the particles,
present in real biological systems. In more realistic models
the inter-particle interaction has been taken into account
through the fact that the birth and death of individuals
depends on the spacial distribution of the bugs:
the birth and death rates of the bugs were assumed to
be functions of the number of neighbors within a given
distance of each bug.
At the same time, it is known that many systems
are characterized by anomalous diffusion, i.e., the mean
square displacement does not grow linearly in time as in
the case of normal Brownian motion, but slower (subdiffusion)
or faster (superdiffusion). In particular, it has
been reported that bacterial motion is described by Lévy
statistics, as well as the movement of spider monkeys in
search of food. Motivated by this we investigate how the
occurrence of the long jumps of the individuals influences
the collective behavior.