Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between ...spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network's components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component. We identify a metastable domain in the global network phase diagram spanned by the model's control parameters where dramatic hysteresis effects and random switching between two coexisting states are observed. This dynamics depends on the characteristic link length of the embedded system. For the Euclidean lattice in particular, hysteresis and switching only occur in an extremely narrow region of the parameter space compared to random networks. We develop a unifying theory which links the dynamics of our model to contact processes. Our unifying framework may help to better understand controllability in spatially embedded and random networks where spontaneous recovery of components can mitigate spontaneous failure and damage spread in dynamical networks.
Recovery of Interdependent Networks Di Muro, M A; La Rocca, C E; Stanley, H E ...
Scientific reports,
03/2016, Volume:
6, Issue:
1
Journal Article
Peer reviewed
Open access
Recent network research has focused on the cascading failures in a system of interdependent networks and the necessary preconditions for system collapse. An important question that has not been ...addressed is how to repair a failing system before it suffers total breakdown. Here we introduce a recovery strategy for nodes and develop an analytic and numerical framework for studying the concurrent failure and recovery of a system of interdependent networks based on an efficient and practically reasonable strategy. Our strategy consists of repairing a fraction of failed nodes, with probability of recovery γ, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction 1 - p of nodes, there is a critical probability of recovery above which the cascade is halted and the system fully restores to its initial state and below which the system abruptly collapses. As a consequence we find in the plane γ - p of the phase diagram three distinct phases. A phase in which the system never collapses without being restored, another phase in which the recovery strategy avoids the breakdown, and a phase in which even the repairing process cannot prevent system collapse.
Many real-world networks interact with and depend upon other networks. We develop an analytical framework for studying a network formed by n fully interdependent randomly connected networks, each ...composed of the same number of nodes N. The dependency links connecting nodes from different networks establish a unique one-to-one correspondence between the nodes of one network and the nodes of the other network. We study the dynamics of the cascades of failures in such a network of networks (NON) caused by a random initial attack on one of the networks, after which a fraction p of its nodes survives. We find for the fully interdependent loopless NON that the final state of the NON does not depend on the dynamics of the cascades but is determined by a uniquely defined mutual giant component of the NON, which generalizes both the giant component of regular percolation of a single network (n=1) and the recently studied case of the mutual giant component of two interdependent networks (n=2). We also find that the mutual giant component does not depend on the topology of the NON and express it in terms of generating functions of the degree distributions of the network. Our results show that, for any n≥2 there exists a critical p=p(c)>0 below which the mutual giant component abruptly collapses from a finite nonzero value for p≥p(c) to zero for p<p(c), as in a first-order phase transition. This behavior holds even for scale-free networks where p(c)=0 for n=1. We show that, if at least one of the networks in the NON has isolated or singly connected nodes, the NON completely disintegrates for sufficiently large n even if p=1. In contrast, in the absence of such nodes, the NON survives for any n for sufficiently large p. We illustrate this behavior by comparing two exactly solvable examples of NONs composed of Erdős-Rényi (ER) and random regular (RR) networks. We find that the robustness of n coupled RR networks of degree k is dramatically higher compared to the n-coupled ER networks of the same average degree kover ¯=k. While for ER NONs there exists a critical minimum average degree kover ¯=kover ¯(min)∼lnn below which the system collapses, for RR NONs k(min)=2 for any n (i.e., for any k>2, a RR NON is stable for any n with p(c)<1). This results arises from the critical role played by singly connected nodes which exist in an ER NON and enhance the cascading failures, but do not exist in a RR NON.
How to prevent the spread of human diseases is a great challenge for the scientific community and so far there are many studies in which immunization strategies have been developed. However, these ...kind of strategies usually do not consider that medical institutes may have limited vaccine resources available. In this manuscript, we explore the susceptible-infected-recovered model with local dynamic vaccination, and considering limited vaccines. In this model, susceptibles in contact with an infected individual, are vaccinated -with probability - and then get infected -with probability β. However, when the fraction of immunized individuals reaches a threshold VL, the vaccination stops, after which only the infection is possible. In the steady state, besides the critical points βc and c that separate a non-epidemic from an epidemic phase, we find for a range of VL another transition points, β* > βc and * < c, which correspond to a novel discontinuous phase transition. This critical value separates a phase where the amount of vaccines is sufficient, from a phase where the disease is strong enough to exhaust all the vaccination units. For a disease with fixed β, the vaccination probability can be controlled in order to drastically reduce the number of infected individuals, using efficiently the available vaccines. Furthermore, the temporal evolution of the system close to β* or *, shows that after a peak of infection the system enters into a quasi-stationary state, with only a few infected cases. But if there are no more vaccines, these few infected individuals could originate a second outbreak, represented by a second peak of infection. This state of apparent calm, could be dangerous since it may lead to misleading conclusions and to an abandon of the strategies to control the disease.
We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used ...efficient market hypothesis. We derive macroscopic equations based on the microscopic herding interactions of agents and find that they are able to reproduce various stylized facts of different markets and different assets with the same set of model parameters. We show that the power-law properties and the scaling of return intervals and other financial variables have a similar origin and could be a result of a general class of non-linear stochastic differential equations derived from a master equation of an agent system that is coupled by herding interactions. Specifically, we find that this approach enables us to recover the volatility return interval statistics as well as volatility probability and spectral densities for the NYSE and FOREX markets, for different assets, and for different time-scales. We find also that the historical S&P500 monthly series exhibits the same volatility return interval properties recovered by our proposed model. Our statistical results suggest that human herding is so strong that it persists even when other evolving fluctuations perturbate the financial system.
•The scaling and memory in financial volatility return intervals are explained.•The method is based on the consentaneous agent based and stochastic model.•The key ingredient of the model is interplay of endogenous and exogenous fluctuations.•Endogenous market dynamics is based on the herding interactions of traders.•Order flow fluctuations are assumed as a source of exogenous noise.
The pattern of local daily fluctuations of climate fields such as temperatures and geopotential heights is not stable and hard to predict. Surprisingly, we find that the observed relations between ...such fluctuations in different geographical regions yields a very robust network pattern that remains highly stable during time. Using a new systematic methodology we track the origins of the network stability. It is found that about half of this network stability is due to the spatial 2D embedding of the network, and half is due to physical coupling between climate in different locations. We also find that around the equator, the contribution of the physical coupling is significantly less pronounced compared to off-equatorial regimes. Finally, we show that there is a gradual monotonic modification of the network pattern as a function of altitude difference.
PDF
