106 research outputs found
Linear and nonlinear information flow in spatially extended systems
Infinitesimal and finite amplitude error propagation in spatially extended
systems are numerically and theoretically investigated. The information
transport in these systems can be characterized in terms of the propagation
velocity of perturbations . A linear stability analysis is sufficient to
capture all the relevant aspects associated to propagation of infinitesimal
disturbances. In particular, this analysis gives the propagation velocity
of infinitesimal errors. If linear mechanisms prevail on the nonlinear ones
. On the contrary, if nonlinear effects are predominant finite
amplitude disturbances can eventually propagate faster than infinitesimal ones
(i.e. ). The finite size Lyapunov exponent can be successfully
employed to discriminate the linear or nonlinear origin of information flow. A
generalization of finite size Lyapunov exponent to a comoving reference frame
allows to state a marginal stability criterion able to provide both in
the linear and in the nonlinear case. Strong analogies are found between
information spreading and propagation of fronts connecting steady states in
reaction-diffusion systems. The analysis of the common characteristics of these
two phenomena leads to a better understanding of the role played by linear and
nonlinear mechanisms for the flow of information in spatially extended systems.Comment: 14 RevTeX pages with 13 eps figures, title/abstract changed minor
changes in the text accepted for publication on PR
Synchronization of extended chaotic systems with long-range interactions: an analogy to Levy-flight spreading of epidemics
Spatially extended chaotic systems with power-law decaying interactions are
considered. Two coupled replicas of such systems synchronize to a common
spatio-temporal chaotic state above a certain coupling strength. The
synchronization transition is studied as a nonequilibrium phase transition and
its critical properties are analyzed at varying the interaction range. The
transition is found to be always continuous, while the critical indexes vary
with continuity with the power law exponent characterizing the interaction.
Strong numerical evidences indicate that the transition belongs to the {\it
anomalous directed percolation} family of universality classes found for
L{\'e}vy-flight spreading of epidemic processes.Comment: 4 revTeX4.0 pages, 3 color figs;added references and minor
changes;Revised version accepted for pubblication on PR
The role of the number of degrees of freedom and chaos in macroscopic irreversibility
This article aims at revisiting, with the aid of simple and neat numerical
examples, some of the basic features of macroscopic irreversibility, and, thus,
of the mechanical foundation of the second principle of thermodynamics as drawn
by Boltzmann. Emphasis will be put on the fact that, in systems characterized
by a very large number of degrees of freedom, irreversibility is already
manifest at a single-trajectory level for the vast majority of the
far-from-equilibrium initial conditions - a property often referred to as
typicality. We also discuss the importance of the interaction among the
microscopic constituents of the system and the irrelevance of chaos to
irreversibility, showing that the same irreversible behaviours can be observed
both in chaotic and non-chaotic systems.Comment: 21 pages, 6 figures, accepted for publication in Physica
Invasions in heterogeneous habitats in the presence of advection
We investigate invasions from a biological reservoir to an initially empty,
heterogeneous habitat in the presence of advection. The habitat consists of a
periodic alternation of favorable and unfavorable patches. In the latter the
population dies at fixed rate. In the former it grows either with the logistic
or with an Allee effect type dynamics, where the population has to overcome a
threshold to grow. We study the conditions for successful invasions and the
speed of the invasion process, which is numerically and analytically
investigated in several limits. Generically advection enhances the downstream
invasion speed but decreases the population size of the invading species, and
can even inhibit the invasion process. Remarkably, however, the rate of
population increase, which quantifies the invasion efficiency, is maximized by
an optimal advection velocity. In models with Allee effect, differently from
the logistic case, above a critical unfavorable patch size the population
localizes in a favorable patch, being unable to invade the habitat. However, we
show that advection, when intense enough, may activate the invasion process.Comment: 16 pages, 11 figures J. Theor. Biol. to appea
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