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Dynamics of threshold network on non-trivial distribution degree

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Abstract.

The dynamics of a threshold network (TN) with thermal noise on scale-free, random-graph, and small-world topologies are considered herein. The present analytical study clarifies that there is no phase transition independent of network structure if temperature T = 0, threshold h = 0 and the probability distribution degree P(k) satisfies P(0) = D = 0. The emergence of phase transition involving three parameters, T, h and D is also investigated. We find that a TN with moderate thermal noise extends the regime of ordered dynamics, compared to a TN in the T = 0 regime or a Random Boolean Network (RBN). A TN can be continuously reduced to an expression of RBN in the infinite T limit.

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Authors and Affiliations

  1. Sony Corporation, 2-10-14 Osaki, Shinagawa, Tokyo, Japan

    I. Nakamura

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  1. I. Nakamura
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Correspondence to I. Nakamura.

Additional information

Received: 25 February 2004, Published online: 12 August 2004

PACS:

89.75.Fb Structures and organization in complex systems - 89.20.Hh World Wide Web, Internet - 05.70.Fh Phase transitions: general studies

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Nakamura, I. Dynamics of threshold network on non-trivial distribution degree. Eur. Phys. J. B 40, 217–221 (2004). https://doi.org/10.1140/epjb/e2004-00260-4

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