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Lin Y, Burghardt K, Rohden M, Noël PA, D'Souza RM. Self-organization of dragon king failures. Phys Rev E 2018; 98:022127. [PMID: 30253566 DOI: 10.1103/physreve.98.022127] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2017] [Indexed: 11/07/2022]
Abstract
The mechanisms underlying cascading failures are often modeled via the paradigm of self-organized criticality. Here we introduce a simple network model where nodes self-organize to be either weakly or strongly protected against failure in a manner that captures the trade-off between degradation and reinforcement of nodes inherent in many network systems. If strong nodes cannot fail, any failure is contained to a single, isolated cluster of weak nodes and the model produces power-law distributions of failure sizes. We classify the large, rare events that involve the failure of only a single cluster as "black swans." In contrast, if strong nodes fail once a sufficient fraction of their neighbors fail, then failure can cascade across multiple clusters of weak nodes. If over 99.9% of the nodes fail due to this cluster hopping mechanism, we classify this as a "dragon king," which are massive failures caused by mechanisms distinct from smaller failures. The dragon kings observed are self-organized, existing over a wide range of reinforcement rates and system sizes. We find that once an initial cluster of failing weak nodes is above a critical size, the dragon king mechanism kicks in, leading to piggybacking system-wide failures. We demonstrate that the size of the initial failed weak cluster predicts the likelihood of a dragon king event with high accuracy and we develop a simple control strategy that can dramatically reduce dragon kings and other large failures.
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Affiliation(s)
- Yuansheng Lin
- School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China.,Beijing Jingdong Century Trade Co., Ltd., Beijing 101111, China.,Department of Computer Science, University of California, Davis, California 95616, USA
| | - Keith Burghardt
- Information Sciences Institute, University of Southern California, Marina del Rey, California 90292, USA
| | - Martin Rohden
- Department of Computer Science, University of California, Davis, California 95616, USA
| | - Pierre-André Noël
- Department of Computer Science, University of California, Davis, California 95616, USA
| | - Raissa M D'Souza
- Department of Computer Science, University of California, Davis, California 95616, USA.,Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616, USA.,Santa Fe Institute, Santa Fe, New Mexico 87501, USA
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Milovanov AV, Rasmussen JJ. Lévy flights on a comb and the plasma staircase. Phys Rev E 2018; 98:022208. [PMID: 30253554 DOI: 10.1103/physreve.98.022208] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2018] [Indexed: 11/07/2022]
Abstract
We formulate the problem of confined Lévy flight on a comb. The comb represents a sawtoothlike potential field V(x), with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law dependence V(x)∝|Δx|^{n} within the sawtooth period, followed by an abrupt drop-off to zero, after which the initial power-law dependence is reset. It is found that the Lévy flights will be confined in the sense of generalized central limit theorem if (i) the spacing between the teeth is sufficiently broad, and (ii) n>4-μ, where μ is the fractal dimension of the flights. In particular, for the Cauchy flights (μ=1), n>3. The study is motivated by recent observations of localization-delocalization of transport avalanches in banded flows in the Tore Supra tokamak and is intended to devise a theory basis to explain the observed phenomenology.
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Affiliation(s)
- Alexander V Milovanov
- ENEA National Laboratory, Centro Ricerche Frascati, I-00044 Frascati, Rome, Italy.,Space Research Institute, Russian Academy of Sciences, 117997 Moscow, Russia
| | - Jens Juul Rasmussen
- Physics Department, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
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Mishra A, Saha S, Vigneshwaran M, Pal P, Kapitaniak T, Dana SK. Dragon-king-like extreme events in coupled bursting neurons. Phys Rev E 2018; 97:062311. [PMID: 30011519 DOI: 10.1103/physreve.97.062311] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Indexed: 06/08/2023]
Abstract
We present evidence of extreme events in two Hindmarsh-Rose (HR) bursting neurons mutually interacting via two different coupling configurations: chemical synaptic- and gap junctional-type diffusive coupling. A dragon-king-like probability distribution of the extreme events is seen for combinations of synaptic coupling where small- to medium-size events obey a power law and the larger events that cross an extreme limit are outliers. The extreme events originate due to instability in antiphase synchronization of the coupled systems via two different routes, intermittency and quasiperiodicity routes to complex dynamics for purely excitatory and inhibitory chemical synaptic coupling, respectively. For a mixed type of inhibitory and excitatory chemical synaptic interactions, the intermittency route to extreme events is only seen. Extreme events with our suggested distribution is also seen for gap junctional-type diffusive, but repulsive, coupling where the intermittency route to complexity is found. A simple electronic experiment using two diffusively coupled analog circuits of the HR neuron model, but interacting in a repulsive way, confirms occurrence of the dragon-king-like extreme events.
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Affiliation(s)
- Arindam Mishra
- Department of Physics, Jadavpur University, Jadavpur, Kolkata 700032, India
| | - Suman Saha
- Department of Mathematics, Jadavpur University, Jadavpur, Kolkata 700032, India
| | - M Vigneshwaran
- CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032, India
| | - Pinaki Pal
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Syamal K Dana
- Department of Mathematics, Jadavpur University, Jadavpur, Kolkata 700032, India
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