5 research outputs found
Nonextensivity of the cyclic Lattice Lotka Volterra model
We numerically show that the Lattice Lotka-Volterra model, when realized on a
square lattice support, gives rise to a {\it finite} production, per unit time,
of the nonextensive entropy . This finiteness only occurs for for the growth mode
(growing droplet), and for for the one (growing stripe). This
strong evidence of nonextensivity is consistent with the spontaneous emergence
of local domains of identical particles with fractal boundaries and competing
interactions. Such direct evidence is for the first time exhibited for a
many-body system which, at the mean field level, is conservative.Comment: Latex, 6 pages, 5 figure
Phase transition and selection in a four-species cyclic Lotka-Volterra model
We study a four species ecological system with cyclic dominance whose
individuals are distributed on a square lattice. Randomly chosen individuals
migrate to one of the neighboring sites if it is empty or invade this site if
occupied by their prey. The cyclic dominance maintains the coexistence of all
the four species if the concentration of vacant sites is lower than a threshold
value. Above the treshold, a symmetry breaking ordering occurs via growing
domains containing only two neutral species inside. These two neutral species
can protect each other from the external invaders (predators) and extend their
common territory. According to our Monte Carlo simulations the observed phase
transition is equivalent to those found in spreading models with two equivalent
absorbing states although the present model has continuous sets of absorbing
states with different portions of the two neutral species. The selection
mechanism yielding symmetric phases is related to the domain growth process
whith wide boundaries where the four species coexist.Comment: 4 pages, 5 figure
Analysis of a spatial Lotka-Volterra model with a finite range predator-prey interaction
We perform an analysis of a recent spatial version of the classical
Lotka-Volterra model, where a finite scale controls individuals' interaction.
We study the behavior of the predator-prey dynamics in physical spaces higher
than one, showing how spatial patterns can emerge for some values of the
interaction range and of the diffusion parameter.Comment: 7 pages, 7 figure
Oscillations and dynamics in a two-dimensional prey-predator system
Using Monte Carlo simulations we study two-dimensional prey-predator systems.
Measuring the variance of densities of prey and predators on the triangular
lattice and on the lattice with eight neighbours, we conclude that temporal
oscillations of these densities vanish in the thermodynamic limit. This result
suggests that such oscillations do not exist in two-dimensional models, at
least when driven by local dynamics. Depending on the control parameter, the
model could be either in an active or in an absorbing phase, which are
separated by the critical point. The critical behaviour of this model is
studied using the dynamical Monte Carlo method. This model has two dynamically
nonsymmetric absorbing states. In principle both absorbing states can be used
for the analysis of the critical point. However, dynamical simulations which
start from the unstable absorbing state suffer from metastable-like effects,
which sometimes renders the method inefficient.Comment: 7 eps figures, Phys.Rev.E - in pres
Lattice Lotka-Volterra model with long range mixing
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion, 05.45.-a Nonlinear dynamics and chaos, 64.60.Ht Dynamic critical phenomena,