- Access by Xinjiang University
Demographic fluctuations in a population of anomalously diffusing individuals
Phys. Rev. E 85, 021125 – Published 21 February, 2012
DOI: https://doi.org/10.1103/PhysRevE.85.021125
Abstract
The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically. The possibility of social behaviors affecting the migration strategies has been taken into exam, in the case that anomalous diffusion is produced by means of a continuous time random walk (CTRW). In the case of independently diffusing individuals, the dynamics appears to coincide with that of (dying and reproducing) Brownian walkers. In the strongly social case, the dynamics coincides with that of nonmigrating individuals. In both limits, the growth rate of the fluctuations becomes independent of the Hurst exponent of the CTRW. The social behaviors that arise when transport in a population is induced by a spatial distribution of random traps have been analyzed.
Article Text
References (21)
- Y.-C. Zhang, M. Serva, and M. Polikarpov, J. Stat. Phys. 58, 849 (1990).
- M. Meyer, S. Havlin, and A. Bunde, Phys. Rev. E 54, 5567 (1996).
- W. R. Young, A. J. Roberts, and G. Stuhne, Nature (London) 412, 328 (2001).
- M. Paesens and G. M. Schütz, J. Phys. A 37, 4709 (2004).
- A. Provenzale, Annu. Rev. Fluid Mech. 31, 55 (1999).
- A. Zoia, Phys. Rev. E 77, 041115 (2008).
- K. C. Leptos, J. S. Guasto, J. P. Gollub, A. I. Pesci, and R. E. Goldstein, Phys. Rev. Lett. 103, 198103 (2009).
- D. W. Sims et al., Nature (London) 451, 1098 (2008).
- J. Klafter, A. Blumen, and M. F. Shlesinger, Phys. Rev. A 35, 3081 (1987).
- H. Hinrichsen and M. Howard, Eur. Phys. J. B 7, 635 (1999).
- J. P. Bouchaud and A. Georges, Phys. Rep. 195, 128 (1990).
- H. Hinrichsen, Adv. Phys. 49, 815 (2000).
- S. B. Yuste, J. J. Ruiz-Lorenzo, and K. Lindenberg, Phys. Rev. E 80, 051114 (2009).
- E. W. Montroll and G. H. Weiss, J. Math. Phys. 6, 167 (1965).
- B. Houchmandzadeh, Phys. Rev. E 66, 052902 (2002).
- M. G. W. Schmidt, F. Sagues, and I. M. Sokolov, J. Phys. Condens. Matter 19, 065118 (2007).
- T. Harris, The Theory of Branching Processes (Springer-Verlag, Berlin, 1963).
- This property is lost in the case of Brownian bugs, in which case Eq. (22) becomes .
- For a total population , the global fluctuation amplitude can be estimated using Eq. (21): .
- E. Heinsalu, E. Hernández-García, and C. López, Europhys. Lett. 92, 40011 (2010).
- J. Beran, Statistics for Long-Memory Processes (Chapman & Hall, London, 1994).