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.
[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) Search in Google Scholar
[2] J. D. Murray, Mathematical Biology, Vol. 1, Third Edition, (Barcelona, Springer, Berlin, 2007) Search in Google Scholar
[3] C. Benkert, D.Z. Anderson, Phys. Rev. A 44, 4633 (1991) http://dx.doi.org/10.1103/PhysRevA.44.463310.1103/PhysRevA.44.4633Search in Google Scholar
[4] C. I. Pistorius, J. M. Utterback, Res. Policy 26, 67 (1997) http://dx.doi.org/10.1016/S0048-7333(96)00916-X10.1016/S0048-7333(96)00916-XSearch in Google Scholar
[5] W. Ebeling, A. Sharnhorst, Adv. Complex Syst. 4, 71 (2001) http://dx.doi.org/10.1142/S021952590100013910.1142/S0219525901000139Search in Google Scholar
[6] M. A. Fuentes, M. N. Kuperman, V. M. Kenkre, Phys. Rev. Lett. 91, 1581041 (2003) 10.1103/PhysRevLett.91.158104Search in Google Scholar PubMed
[7] M. A. Fuentes, M. N. Kuperman, V. M. Kenkre, J. Phys. Chem. B 108, 10505 (2004) http://dx.doi.org/10.1021/jp040090k10.1021/jp040090kSearch in Google Scholar
[8] J. Garcia-Ojalvo, J. M. Sancho, Noise in Spatially Extended, Systems, (Springer, Berlin 2010) Search in 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) Search in Google Scholar
[10] M. O. Cáceres. J. Stat. Phys. 132, 487 (2008) http://dx.doi.org/10.1007/s10955-008-9554-710.1007/s10955-008-9554-7Search in 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 10.1007/978-94-011-3442-2_13Search in Google Scholar
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