Dynamical Response of Networks Under External Perturbations: Exact Results

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• 作者：David D. Chinellato (1)
  Irving R. Epstein (2) (3)
  Dan Braha (2) (4)
  Yaneer Bar-Yam (2)
  Marcus A. M. de Aguiar (1) (2)
  
  1. Instituto de F铆sica 鈥楪leb Wataghin鈥? Universidade Estadual de Campinas ; Unicamp ; Campinas ; SP ; 13083-970 ; Brazil
  2. New England Complex Systems Institute ; Cambridge ; MA ; 02138 ; USA
  3. Department of Chemistry ; MS015 ; Brandeis University ; Waltham ; MA ; 02454 ; USA
  4. University of Massachusetts ; Dartmouth ; MA ; 02747 ; USA
  
• 关键词：Networks ; Finite systems ; Voter model ; External perturbations ; Ising model
• 刊名：Journal of Statistical Physics
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：159
• 期：2
• 页码：221-230
• 全文大小：292 KB
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• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

We give exact statistical distributions for the dynamic response of influence networks subjected to external perturbations. We consider networks whose nodes have two internal states labeled 0 and 1. We let \(N_0\) nodes be frozen in state 0, \(N_1\) in state 1, and the remaining nodes change by adopting the state of a connected node with a fixed probability per time step. The frozen nodes can be interpreted as external perturbations to the subnetwork of free nodes. Analytically extending \(N_0\) and \(N_1\) to be smaller than 1 enables modeling the case of weak coupling. We solve the dynamical equations exactly for fully connected networks, obtaining the equilibrium distribution, transition probabilities between any two states and the characteristic time to equilibration. Our exact results are excellent approximations for other topologies, including random, regular lattice, scale-free and small world networks, when the numbers of fixed nodes are adjusted to take account of the effect of topology on coupling to the environment. This model can describe a variety of complex systems, from magnetic spins to social networks to population genetics, and was recently applied as a framework for early warning signals for real-world self-organized economic market crises.