120 research outputs found
Stochastic resonance in bistable systems: The effect of simultaneous additive and multiplicative correlated noises
We analyze the effect of the simultaneous presence of correlated additive and
multiplicative noises on the stochastic resonance response of a modulated
bistable system. We find that when the correlation parameter is also modulated,
the system's response, measured through the output signal-to-noise ratio,
becomes largely independent of the additive noise intensity.Comment: RevTex, 10 pgs, 3 figure
Non-universal results induced by diversity distribution in coupled excitable systems
We consider a system of globally coupled active rotators near the excitable
regime. The system displays a transition to a state of collective firing
induced by disorder. We show that this transition is found generically for any
diversity distribution with well defined moments. Singularly, for the
Lorentzian distribution (widely used in Kuramoto-like systems) the transition
is not present. This warns about the use of Lorentzian distributions to
understand the generic properties of coupled oscillators
How big is too big? Critical Shocks for Systemic Failure Cascades
External or internal shocks may lead to the collapse of a system consisting
of many agents. If the shock hits only one agent initially and causes it to
fail, this can induce a cascade of failures among neighoring agents. Several
critical constellations determine whether this cascade remains finite or
reaches the size of the system, i.e. leads to systemic risk. We investigate the
critical parameters for such cascades in a simple model, where agents are
characterized by an individual threshold \theta_i determining their capacity to
handle a load \alpha\theta_i with 1-\alpha being their safety margin. If agents
fail, they redistribute their load equally to K neighboring agents in a regular
network. For three different threshold distributions P(\theta), we derive
analytical results for the size of the cascade, X(t), which is regarded as a
measure of systemic risk, and the time when it stops. We focus on two different
regimes, (i) EEE, an external extreme event where the size of the shock is of
the order of the total capacity of the network, and (ii) RIE, a random internal
event where the size of the shock is of the order of the capacity of an agent.
We find that even for large extreme events that exceed the capacity of the
network finite cascades are still possible, if a power-law threshold
distribution is assumed. On the other hand, even small random fluctuations may
lead to full cascades if critical conditions are met. Most importantly, we
demonstrate that the size of the "big" shock is not the problem, as the
systemic risk only varies slightly for changes of 10 to 50 percent of the
external shock. Systemic risk depends much more on ingredients such as the
network topology, the safety margin and the threshold distribution, which gives
hints on how to reduce systemic risk.Comment: 23 pages, 7 Figure
Chaotic synchronizations of spatially extended systems as non-equilibrium phase transitions
Two replicas of spatially extended chaotic systems synchronize to a common
spatio-temporal chaotic state when coupled above a critical strength. As a
prototype of each single spatio-temporal chaotic system a lattice of maps
interacting via power-law coupling is considered. The synchronization
transition is studied as a non-equilibrium phase transition, and its critical
properties are analyzed at varying the spatial interaction range as well as the
nonlinearity of the dynamical units composing each system. In particular,
continuous and discontinuous local maps are considered. In both cases the
transitions are of the second order with critical indexes varying with the
exponent characterizing the interaction range. For discontinuous maps it is
numerically shown that the transition belongs to the {\it anomalous directed
percolation} (ADP) family of universality classes, previously identified for
L{\'e}vy-flight spreading of epidemic processes. For continuous maps, the
critical exponents are different from those characterizing ADP, but apart from
the nearest-neighbor case, the identification of the corresponding universality
classes remains an open problem. Finally, to test the influence of
deterministic correlations for the studied synchronization transitions, the
chaotic dynamical evolutions are substituted by suitable stochastic models. In
this framework and for the discontinuous case, it is possible to derive an
effective Langevin description that corresponds to that proposed for ADP.Comment: 12 pages, 5 figures Comments are welcom
Evolutionary and Ecological Trees and Networks
Evolutionary relationships between species are usually represented in
phylogenies, i.e. evolutionary trees, which are a type of networks. The
terminal nodes of these trees represent species, which are made of individuals
and populations among which gene flow occurs. This flow can also be represented
as a network. In this paper we briefly show some properties of these complex
networks of evolutionary and ecological relationships. First, we characterize
large scale evolutionary relationships in the Tree of Life by a degree
distribution. Second, we represent genetic relationships between individuals of
a Mediterranean marine plant, Posidonia oceanica, in terms of a Minimum
Spanning Tree. Finally, relationships among plant shoots inside populations are
represented as networks of genetic similarity.Comment: 6 pages, 5 figures. To appear in Proceedings of the Medyfinol06
Conferenc
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