16 research outputs found
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
Multiplicative noise: A mechanism leading to nonextensive statistical mechanics
A large variety of microscopic or mesoscopic models lead to generic results
that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based
on ). Similarly, other classes of models
point toward nonextensive statistical mechanics (based on , where the value of the entropic index depends on
the specific model). We show here a family of models, with multiplicative
noise, which belongs to the nonextensive class. More specifically, we consider
Langevin equations of the type , where
and are independent zero-mean Gaussian white noises with
respective amplitudes and . This leads to the Fokker-Planck equation
. Whenever the
deterministic drift is proportional to the noise induced one, i.e., , the stationary solution is shown to be (with and ). This distribution is
precisely the one optimizing with the constraint constant. We also
introduce and discuss various characterizations of the width of the
distributions.Comment: 3 PS figure
From 2000 Bush-Gore to 2006 Italian elections: Voting at fifty-fifty and the Contrarian Effect
A sociophysical model for opinion dynamics is shown to embody a series of
recent western hung national votes all set at the unexpected and very
improbable edge of a fifty-fifty score. It started with the Bush-Gore 2000
American presidential election, followed by the 2002 Stoiber-Schr\H{o}der, then
the 2005 Schr\H{o}der-Merkel German elections, and finally the 2006
Prodi-Berlusconi Italian elections. In each case, the country was facing
drastic choices, the running competing parties were advocating very different
programs and millions of voters were involved. Moreover, polls were given a
substantial margin for the predicted winner. While all these events were
perceived as accidental and isolated, our model suggests that indeed they are
deterministic and obey to one single universal phenomena associated to the
effect of contrarian behavior on the dynamics of opinion forming. The not hung
Bush-Kerry 2005 presidential election is shown to belong to the same universal
frame. To conclude, the existence of contrarians hints at the repetition of
hung elections in the near future.Comment: 17 pages, 8 figure
On the Influence of Noise on the Critical and Oscillatory Behavior of a Predator-Prey Model: Coherent Stochastic Resonance at the Proper Frequency
Noise induced changes in the critical and oscillatory behavior of a
Prey-Predator system are studied using power spectrum density and Spectral
Amplification Factor (SAF) analysis. In the absence of external noise, the
population densities exhibit three kinds of asymptotic behavior, namely:
Absorbing State, Fixed Point (FP) and an Oscillatory Regime (OR) with a well
defined proper (natural) frequency. The addition of noise destabilizes the FP
phase inducing a transition to a new OR. Surprisingly, it is found that when a
periodic signal is added to the control parameter, the system responds
robustly, without relevant changes in its behavior. Nevertheless, the "Coherent
Stochastic Resonance" phenomenon is found only at the proper frequency. Also, a
method based on SAF allows us to locate very accurately the transition points
between the different regimes.Comment: RevTex, 18 pgs, 6 figures. Submitted to Physics Letters A (2000
Opinion dynamics: models, extensions and external effects
Recently, social phenomena have received a lot of attention not only from
social scientists, but also from physicists, mathematicians and computer
scientists, in the emerging interdisciplinary field of complex system science.
Opinion dynamics is one of the processes studied, since opinions are the
drivers of human behaviour, and play a crucial role in many global challenges
that our complex world and societies are facing: global financial crises,
global pandemics, growth of cities, urbanisation and migration patterns, and
last but not least important, climate change and environmental sustainability
and protection. Opinion formation is a complex process affected by the
interplay of different elements, including the individual predisposition, the
influence of positive and negative peer interaction (social networks playing a
crucial role in this respect), the information each individual is exposed to,
and many others. Several models inspired from those in use in physics have been
developed to encompass many of these elements, and to allow for the
identification of the mechanisms involved in the opinion formation process and
the understanding of their role, with the practical aim of simulating opinion
formation and spreading under various conditions. These modelling schemes range
from binary simple models such as the voter model, to multi-dimensional
continuous approaches. Here, we provide a review of recent methods, focusing on
models employing both peer interaction and external information, and
emphasising the role that less studied mechanisms, such as disagreement, has in
driving the opinion dynamics. [...]Comment: 42 pages, 6 figure