537 research outputs found
Very long transients in globally coupled maps
Very long transients are found in the partially ordered phase of type II of
globally coupled logistic maps. The transients always lead the system in this
phase to a state with a few synchronous clusters. This transient behaviour is
not significantly influenced by the introduction of weak noises. However, such
noises generally favor cluster partitions with more stable periodic dynamics.Comment: 4 pages, 5 figures include
Demography-based adaptive network model reproduces the spatial organization of human linguistic groups
The distribution of human linguistic groups presents a number of interesting
and non-trivial patterns. The distributions of the number of speakers per
language and the area each group covers follow log-normal distributions, while
population and area fulfill an allometric relationship. The topology of
networks of spatial contacts between different linguistic groups has been
recently characterized, showing atypical properties of the degree distribution
and clustering, among others. Human demography, spatial conflicts, and the
construction of networks of contacts between linguistic groups are mutually
dependent processes. Here we introduce an adaptive network model that takes all
of them into account and successfully reproduces, using only four model
parameters, not only those features of linguistic groups already described in
the literature, but also correlations between demographic and topological
properties uncovered in this work. Besides their relevance when modeling and
understanding processes related to human biogeography, our adaptive network
model admits a number of generalizations that broaden its scope and make it
suitable to represent interactions between agents based on population dynamics
and competition for space
Neutral networks of genotypes: Evolution behind the curtain
Our understanding of the evolutionary process has gone a long way since the
publication, 150 years ago, of "On the origin of species" by Charles R. Darwin.
The XXth Century witnessed great efforts to embrace replication, mutation, and
selection within the framework of a formal theory, able eventually to predict
the dynamics and fate of evolving populations. However, a large body of
empirical evidence collected over the last decades strongly suggests that some
of the assumptions of those classical models necessitate a deep revision. The
viability of organisms is not dependent on a unique and optimal genotype. The
discovery of huge sets of genotypes (or neutral networks) yielding the same
phenotype --in the last term the same organism--, reveals that, most likely,
very different functional solutions can be found, accessed and fixed in a
population through a low-cost exploration of the space of genomes. The
'evolution behind the curtain' may be the answer to some of the current puzzles
that evolutionary theory faces, like the fast speciation process that is
observed in the fossil record after very long stasis periods.Comment: 7 pages, 7 color figures, uses a modification of pnastwo.cls called
pnastwo-modified.cls (included
Stochastic multiplicative processes with reset events
We study a stochastic multiplicative process with reset events. It is shown
that the model develops a stationary power-law probability distribution for the
relevant variable, whose exponent depends on the model parameters. Two
qualitatively different regimes are observed, corresponding to intermittent and
regular behaviour. In the boundary between them, the mean value of the relevant
variable is time-independent, and the exponent of the stationary distribution
equals -2. The addition of diffusion to the system modifies in a non-trivial
way the profile of the stationary distribution. Numerical and analytical
results are presented.Comment: 8 pages, 3 figures. To appear in Phys. Rev.
Small-world behavior in a system of mobile elements
We analyze the propagation of activity in a system of mobile automata. A
number r L^d of elements move as random walkers on a lattice of dimension d,
while with a small probability p they can jump to any empty site in the system.
We show that this system behaves as a Dynamic Small-World (DSW) and present
analytic and numerical results for several quantities. Our analysis shows that
the persistence time T* (equivalent to the persistence size L* of small-world
networks) scales as T* ~ (r p)^(-t), with t = 1/(d+1).Comment: To appear in Europhysics Letter
Long transients and cluster size in globally coupled maps
We analyze the asymptotic states in the partially ordered phase of a system
of globally coupled logistic maps. We confirm that, regardless of initial
conditions, these states consist of a few clusters, and they properly belong in
the ordered phase of these systems. The transient times necessary to reach the
asymptotic states can be very long, especially very near the transition line
separating the ordered and the coherent phases. We find that, where two
clusters form, the distribution of their sizes corresponds to windows of
regular or narrow-band chaotic behavior in the bifurcation diagram of a system
of two degrees of freedom that describes the motion of two clusters, where the
size of one cluster acts as a bifurcation parameter.Comment: To appear in Europhysics Letter
Biodiversity in model ecosystems, II: Species assembly and food web structure
This is the second of two papers dedicated to the relationship between
population models of competition and biodiversity. Here we consider species
assembly models where the population dynamics is kept far from fixed points
through the continuous introduction of new species, and generalize to such
models thecoexistence condition derived for systems at the fixed point. The
ecological overlap between species with shared preys, that we define here,
provides a quantitative measure of the effective interspecies competition and
of the trophic network topology. We obtain distributions of the overlap from
simulations of a new model based both on immigration and speciation, and show
that they are in good agreement with those measured for three large natural
food webs. As discussed in the first paper, rapid environmental fluctuations,
interacting with the condition for coexistence of competing species, limit the
maximal biodiversity that a trophic level can host. This horizontal limitation
to biodiversity is here combined with either dissipation of energy or growth of
fluctuations, which in our model limit the length of food webs in the vertical
direction. These ingredients yield an effective model of food webs that produce
a biodiversity profile with a maximum at an intermediate trophic level, in
agreement with field studies
- …