Abstract
This chapter reports a critical phenomenon in a self-repair network by mutual copying. Extensive studies have been done on critical phenomena in many fields such as in epidemic theory and in percolation theory in order to identify critical points. However, critical phenomena have hardly been studied from the viewpoint of cleaning up a network by mutual copying. A critical phenomenon has been observed in a self-repair network. Self-repairing by mutual copying is “a double-edged sword” that could cause outbreaks if parameters are inappropriate, and therefore careful investigations are needed.
Most results of this chapter are presented in Ishida (2005).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bagnoli, F., Boccara, N., Palmerini, P.: Phase transitions in a probabilistic cellular automaton with two absorbing states (1997). arXiv preprint cond-mat/9705171
Barabási, A.-L., Frangos, J.: Linked: The New Science of Networks Science of Networks. Basic Books, New York (2002)
Boccara, N., Cheong, K.: Critical-behavior of a probabilistic-automata network SIS model for the spread of an infectious-disease in a population of moving individuals. J. Phys. A Math. Gen. 26(15), 3707–3717 (1993). doi:10.1088/0305-4470/26/15/020
Dezso, Z., Barabási, A.L.: Halting viruses in scale-free networks. Phys. Rev. E 65(5) (2002). doi:10.1103/PhysRevE.65.055103
Domany, E., Kinzel, W.: Equivalence of cellular automata to Ising models and directed percolation. Phys. Rev. Lett. 53(4), 311–314 (1984)
Eloranta, K.: Cellular automata for contour dynamics. Physica D 89(1), 184–203 (1995)
Gacs, P.: Reliable cellular automata with self-organization. J. Stat. Phys. 103(1–2), 45–267 (2001). doi:10.1023/A:1004823720305
Gray, L.F.: A reader’s guide to Gacs’s “Positive Rates” paper. J. Stat. Phys. 103(1–2), 1–44 (2001). doi:10.1023/A:1004824203467
Ishida, Y.: Immunity-Based Systems: A Design Perspective. Springer, New York Incorporated (2004)
Ishida, Y.: A critical phenomenon in a self-repair network by mutual copying. In: Knowledge-Based Intelligent Information and Engineering Systems, pp. 86–92. Springer, Berlin (2005)
Kinzel, W.: Phase transitions of cellular automata. Zeitschrift für Physik B Condensed Matter 58(3), 229–244 (1985)
Rhodes, C.J., Anderson, R.M.: Dynamics in a lattice epidemic model. Phys. Lett. A 210(3), 183–188 (1996). doi:10.1016/S0375-9601(96)80007-7
Rhodes, C.J., Anderson, R.M.: Forest-fire as a model for the dynamics of disease epidemics. J. Franklin Inst. 335B(2), 199–211 (1998). doi:10.1016/S0016-0032(96)00096-8
Vichniac, G., Tamayo, P., Hartman, H.: Annealed and quenched inhomogeneous cellular automata (INCA). J. Stat. Phys. 45(5–6), 875–883 (1986)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Ishida, Y. (2015). A Phase Transition in Self-Repair Networks: Problems and Definitions. In: Self-Repair Networks. Intelligent Systems Reference Library, vol 101. Springer, Cham. https://doi.org/10.1007/978-3-319-26447-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-26447-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26445-5
Online ISBN: 978-3-319-26447-9
eBook Packages: EngineeringEngineering (R0)