David A Kessler and Nadav M Shnerb 2008 J. Phys. A: Math. Theor. 41 292003 doi:10.1088/1751-8113/41/29/292003
Novel exponents control the quasi-deterministic limit of the extinction transition
FREE ARTICLEDavid A Kessler and Nadav M Shnerb
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The quasi-deterministic limit of the generic extinction transition is considered within the framework of standard epidemiological models. The susceptible-infected-susceptible (SIS) model is known to exhibit a transition from extinction to spreading, as the infectivity is increased, described by the directed percolation equivalence class. We find that the distance from the transition point, and the prefactor controlling the divergence of the (perpendicular) correlation length, both scale with the local population size, N, with two novel universal exponents. Different exponents characterize the large-N behavior of the susceptible-infected-recovered (SIR) model, which belongs to the dynamic percolation class. Extensive numerical studies in a range of systems lead to the conjecture that these characteristics are generic and may be used in order to classify the high density limit of any stochastic process on the edge of extinction.
- PACS
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87.23.Cc Population dynamics and ecological pattern formation
05.70.Jk Critical point phenomena
05.70.Fh Phase transitions: general studies
- MSC
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82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
92D25 Population dynamics (general)
82C26 Dynamic and nonequilibrium phase transitions (general)
- Subjects
- Dates
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Issue 29 (25 July 2008)
Received 7 May 2008, in final form 12 June 2008
Published 27 June 2008
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Novel exponents control the quasi-deterministic limit of the extinction transition
David A Kessler and Nadav M Shnerb 2008 J. Phys. A: Math. Theor. 41 292003
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