18,592 research outputs found
Drift- or Fluctuation-Induced Ordering and Self-Organization in Driven Many-Particle Systems
According to empirical observations, some pattern formation phenomena in
driven many-particle systems are more pronounced in the presence of a certain
noise level. We investigate this phenomenon of fluctuation-driven ordering with
a cellular automaton model of interactive motion in space and find an optimal
noise strength, while order breaks down at high(er) fluctuation levels.
Additionally, we discuss the phenomenon of noise- and drift-induced
self-organization in systems that would show disorder in the absence of
fluctuations. In the future, related studies may have applications to the
control of many-particle systems such as the efficient separation of particles.
The rather general formulation of our model in the spirit of game theory may
allow to shed some light on several different kinds of noise-induced ordering
phenomena observed in physical, chemical, biological, and socio-economic
systems (e.g., attractive and repulsive agglomeration, or segregation).Comment: For related work see http://www.helbing.or
Crises and collective socio-economic phenomena: simple models and challenges
Financial and economic history is strewn with bubbles and crashes, booms and
busts, crises and upheavals of all sorts. Understanding the origin of these
events is arguably one of the most important problems in economic theory. In
this paper, we review recent efforts to include heterogeneities and
interactions in models of decision. We argue that the Random Field Ising model
(RFIM) indeed provides a unifying framework to account for many collective
socio-economic phenomena that lead to sudden ruptures and crises. We discuss
different models that can capture potentially destabilising self-referential
feedback loops, induced either by herding, i.e. reference to peers, or
trending, i.e. reference to the past, and account for some of the phenomenology
missing in the standard models. We discuss some empirically testable
predictions of these models, for example robust signatures of RFIM-like herding
effects, or the logarithmic decay of spatial correlations of voting patterns.
One of the most striking result, inspired by statistical physics methods, is
that Adam Smith's invisible hand can badly fail at solving simple coordination
problems. We also insist on the issue of time-scales, that can be extremely
long in some cases, and prevent socially optimal equilibria to be reached. As a
theoretical challenge, the study of so-called "detailed-balance" violating
decision rules is needed to decide whether conclusions based on current models
(that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys; several
minor improvements along reviewers' comment
Fast and slow domino regimes in transient network dynamics
It is well known that the addition of noise to a multistable dynamical system
can induce random transitions from one stable state to another. For low noise,
the times between transitions have an exponential tail and Kramers' formula
gives an expression for the mean escape time in the asymptotic limit. If a
number of multistable systems are coupled into a network structure, a
transition at one site may change the transition properties at other sites. We
study the case of escape from a "quiescent" attractor to an "active" attractor
in which transitions back can be ignored. There are qualitatively different
regimes of transition, depending on coupling strength. For small coupling
strengths the transition rates are simply modified but the transitions remain
stochastic. For large coupling strengths transitions happen approximately in
synchrony - we call this a "fast domino" regime. There is also an intermediate
coupling regime some transitions happen inexorably but with a delay that may be
arbitrarily long - we call this a "slow domino" regime. We characterise these
regimes in the low noise limit in terms of bifurcations of the potential
landscape of a coupled system. We demonstrate the effect of the coupling on the
distribution of timings and (in general) the sequences of escapes of the
system.Comment: 3 figure
Phenomenological Models of Socio-Economic Network Dynamics
We study a general set of models of social network evolution and dynamics.
The models consist of both a dynamics on the network and evolution of the
network. Links are formed preferentially between 'similar' nodes, where the
similarity is defined by the particular process taking place on the network.
The interplay between the two processes produces phase transitions and
hysteresis, as seen using numerical simulations for three specific processes.
We obtain analytic results using mean field approximations, and for a
particular case we derive an exact solution for the network. In common with
real-world social networks, we find coexistence of high and low connectivity
phases and history dependence.Comment: 11 pages, 8 figure
Early warning signs for saddle-escape transitions in complex networks
Many real world systems are at risk of undergoing critical transitions,
leading to sudden qualitative and sometimes irreversible regime shifts. The
development of early warning signals is recognized as a major challenge. Recent
progress builds on a mathematical framework in which a real-world system is
described by a low-dimensional equation system with a small number of key
variables, where the critical transition often corresponds to a bifurcation.
Here we show that in high-dimensional systems, containing many variables, we
frequently encounter an additional non-bifurcative saddle-type mechanism
leading to critical transitions. This generic class of transitions has been
missed in the search for early-warnings up to now. In fact, the saddle-type
mechanism also applies to low-dimensional systems with saddle-dynamics. Near a
saddle a system moves slowly and the state may be perceived as stable over
substantial time periods. We develop an early warning sign for the saddle-type
transition. We illustrate our results in two network models and epidemiological
data. This work thus establishes a connection from critical transitions to
networks and an early warning sign for a new type of critical transition. In
complex models and big data we anticipate that saddle-transitions will be
encountered frequently in the future.Comment: revised versio
Exogenous and endogenous crashes as phase transitions in complex financial systems
In this paper we provide a unifying framework for a set of seemingly disparate models for exogenous and endogenous shocks in complex financial systems. Markets operate by balancing intrinsic levels of risk and return. This remains true even in the midst of transitory external shocks. Changes in market regime (bearish to bullish and bullish to bearish) can be explicitly shown to represent a phase transition from random to deterministic behaviour in prices. The resulting models refine the empirical analysis in a number of previous papers.Exogenous; Endogenous; Financial Crashes; Bubbles; Econophysics
Rate-Induced Transitions in Networked Complex Adaptive Systems: Exploring Dynamics and Management Implications Across Ecological, Social, and Socioecological Systems
Complex adaptive systems (CASs), from ecosystems to economies, are open
systems and inherently dependent on external conditions. While a system can
transition from one state to another based on the magnitude of change in
external conditions, the rate of change -- irrespective of magnitude -- may
also lead to system state changes due to a phenomenon known as a rate-induced
transition (RIT). This study presents a novel framework that captures RITs in
CASs through a local model and a network extension where each node contributes
to the structural adaptability of others. Our findings reveal how RITs occur at
a critical environmental change rate, with lower-degree nodes tipping first due
to fewer connections and reduced adaptive capacity. High-degree nodes tip later
as their adaptability sources (lower-degree nodes) collapse. This pattern
persists across various network structures. Our study calls for an extended
perspective when managing CASs, emphasizing the need to focus not only on
thresholds of external conditions but also the rate at which those conditions
change, particularly in the context of the collapse of surrounding systems that
contribute to the focal system's resilience. Our analytical method opens a path
to designing management policies that mitigate RIT impacts and enhance
resilience in ecological, social, and socioecological systems. These policies
could include controlling environmental change rates, fostering system
adaptability, implementing adaptive management strategies, and building
capacity and knowledge exchange. Our study contributes to the understanding of
RIT dynamics and informs effective management strategies for complex adaptive
systems in the face of rapid environmental change.Comment: 25 pages, 4 figures, 1 box, supplementary informatio
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