143 research outputs found
Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices
We consider the superstable cycles of the Q-state Potts (QSP) and the
three-site interaction antiferromagnetic Ising (TSAI) models on recursive
lattices. The rational mappings describing the models' statistical properties
are obtained via the recurrence relation technique. We provide analytical
solutions for the superstable cycles of the second order for both models. A
particular attention is devoted to the period three window. Here we present an
exact result for the third order superstable orbit for the QSP and a numerical
solution for the TSAI model. Additionally, we point out a non-trivial
connection between bifurcations and superstability: in some regions of
parameters a superstable cycle is not followed by a doubling bifurcation.
Furthermore, we use symbolic dynamics to understand the changes taking place at
points of superstability and to distinguish areas between two consecutive
superstable orbits.Comment: 12 pages, 5 figures. Updated version for publicatio
Window scaling in one-dimensional maps
We describe both the internal structure and the width of the periodic windows in one-dimensional maps, by considering a universal local submap. Both features are found to depend only on the order of the extremum of this submap. Moreover, we discuss how the windows are grouped in accumulating families, and we calculate the scaling of the widths within these families
Hydrodynamic Limit of Brownian Particles Interacting with Short and Long Range Forces
We investigate the time evolution of a model system of interacting particles,
moving in a -dimensional torus. The microscopic dynamics are first order in
time with velocities set equal to the negative gradient of a potential energy
term plus independent Brownian motions: is the sum of pair
potentials, , the second term has the form of a Kac
potential with inverse range . Using diffusive hydrodynamical scaling
(spatial scale , temporal scale ) we obtain, in the
limit , a diffusive type integro-differential equation
describing the time evolution of the macroscopic density profile.Comment: 37 pages, in TeX (compile twice), to appear on J. Stat. Phys., e-mail
addresses: [email protected], [email protected]
Regulation mechanisms in spatial stochastic development models
The aim of this paper is to analyze different regulation mechanisms in
spatial continuous stochastic development models. We describe the density
behavior for models with global mortality and local establishment rates. We
prove that the local self-regulation via a competition mechanism (density
dependent mortality) may suppress a unbounded growth of the averaged density if
the competition kernel is superstable.Comment: 19 page
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