35 research outputs found
Ising model for distribution networks
An elementary Ising spin model is proposed for demonstrating cascading
failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in
realistic networks for distribution and delivery by suppliers to consumers. A
ferromagnetic Hamiltonian with quenched random fields results from policies
that maximize the gap between demand and delivery. Such policies can arise in a
competitive market where firms artificially create new demand, or in a solidary
environment where too high a demand cannot reasonably be met. Network failure
in the context of a policy of solidarity is possible when an initially active
state becomes metastable and decays to a stable inactive state. We explore the
characteristics of the demand and delivery, as well as the topological
properties, which make the distribution network susceptible of failure. An
effective temperature is defined, which governs the strength of the activity
fluctuations which can induce a collapse. Numerical results, obtained by Monte
Carlo simulations of the model on (mainly) scale-free networks, are
supplemented with analytic mean-field approximations to the geometrical random
field fluctuations and the thermal spin fluctuations. The role of hubs versus
poorly connected nodes in initiating the breakdown of network activity is
illustrated and related to model parameters
Dynamical robustness in complex networks: the crucial role of low-degree nodes
Many social, biological, and technological networks consist of a small number of highly connected components (hubs) and a very large number of loosely connected components (low-degree nodes). It has been commonly recognized that such heterogeneously connected networks are extremely vulnerable to the failure of hubs in terms of structural robustness of complex networks. However, little is known about dynamical robustness, which refers to the ability of a network to maintain its dynamical activity against local perturbations. Here we demonstrate that, in contrast to the structural fragility, the nonlinear dynamics of heterogeneously connected networks can be highly vulnerable to the failure of low-degree nodes. The crucial role of low-degree nodes results from dynamical processes where normal (active) units compensate for the failure of neighboring (inactive) units at the expense of a reduction in their own activity. Our finding highlights the significant difference between structural and dynamical robustness in complex networks