Skip to main content
SpringerLink
Log in

First passage time on pattern formation in a non-local Fisher population dynamics

  • Research Article
  • Published:
Central European Journal of Physics

Abstract

We use stochastic dynamics to develop the patterned attractor of a non-local extended system. This is done analytically using the stochastic path perturbation approach scheme, where a theory of perturbation in the small noise parameter is introduced to analyze the random escape of the stochastic field from the unstable state. Emphasis is placed on the specific mode selection that these types of systems exhibit. Concerning the stochastic propagation of the front we have carried out Monte Carlo simulations which coincide with our theoretical predictions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. Volterra, Variazioni e fluttuazioni del numero d’individui in specie animali conciventi (Variations and fluctuations of the number of individuals in animal species living together), Memoria della R. Accademia Nazionale dei Lincei, Ser. VI 2, 31–113. [Translated in Chapman, R. 1931 Animal ecology, pp. 409–448. NY: McGraw Hill] (1926)

    Google Scholar 

  2. J. D. Murray, Mathematical Biology, Vol. 1, Third Edition, (Barcelona, Springer, Berlin, 2007)

    Google Scholar 

  3. C. Benkert, D.Z. Anderson, Phys. Rev. A 44, 4633 (1991)

    Article  ADS  Google Scholar 

  4. C. I. Pistorius, J. M. Utterback, Res. Policy 26, 67 (1997)

    Article  Google Scholar 

  5. W. Ebeling, A. Sharnhorst, Adv. Complex Syst. 4, 71 (2001)

    Article  MATH  Google Scholar 

  6. M. A. Fuentes, M. N. Kuperman, V. M. Kenkre, Phys. Rev. Lett. 91, 1581041 (2003)

    Google Scholar 

  7. M. A. Fuentes, M. N. Kuperman, V. M. Kenkre, J. Phys. Chem. B 108, 10505 (2004)

    Article  Google Scholar 

  8. J. Garcia-Ojalvo, J. M. Sancho, Noise in Spatially Extended, Systems, (Springer, Berlin 2010)

    Google Scholar 

  9. M. O. Cáceres, Elementos de estadistica de no equilibrio y sus aplicaciones al transporte en medios desordenados, in Spanish, (Reverté S.A., Barcelona, 2003)

    Google Scholar 

  10. M. O. Cáceres. J. Stat. Phys. 132, 487 (2008)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. M. San Miguel, H. Hernandez-Garcia, P. Colet, M. O. Cáceres, F. De Pasquale, Instabilities and Nonnequilibrium Structures III, E. Tirapegui, W. Zeller (Eds.), (Kluwer Academic Publishers, 1991), 143

Download references

Author information

Authors and Affiliations

  1. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico, 87501, USA

    Miguel A. Fuentes

  2. Centro Atómico Bariloche, Instituto Balseiro and CONICET, 8400, Bariloche, Argentina

    Miguel A. Fuentes & Manuel O. Cáceres

  3. Centro de Investigación en Complejidad Social, CICS Facultad de Gobierno, Universidad de Desarrollo, Santiago, Chile

    Miguel A. Fuentes

Authors
  1. Miguel A. Fuentes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manuel O. Cáceres
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miguel A. Fuentes.

About this article

Cite this article

Fuentes, M.A., Cáceres, M.O. First passage time on pattern formation in a non-local Fisher population dynamics. centr.eur.j.phys. 11, 1623–1628 (2013). https://doi.org/10.2478/s11534-013-0268-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11534-013-0268-3

Keywords

Search

Navigation