Nonlocal competition and logistic growth: Patterns, defects, and fronts

Yosef E. Maruvka and Nadav M. Shnerb
Phys. Rev. E 73, 011903 – Published 10 January 2006

Abstract

Logistic growth of diffusing reactants on spatial domains with long-range competition is studied. The bifurcations cascade involved in the transition from the homogeneous state to a spatially modulated stable solution is presented, and a distinction is made between a modulated phase, dominated by single or few wave numbers, and the spiky phase, where localized colonies are separated by depleted region. The characteristic defects in the periodic structure are presented for each phase, together with the invasion dynamics in the case of local initiation. It is shown that the basic length scale that controls the bifurcation is the width of the Fisher front, and that the total population grows as this width decreases. A mix of analytic results and extensive numerical simulations yields a comprehensive examination of the possible phases for logistic growth in the presence of nonlocal competition.

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  • Received 12 June 2005

DOI:https://doi.org/10.1103/PhysRevE.73.011903

©2006 American Physical Society

Authors & Affiliations

Yosef E. Maruvka and Nadav M. Shnerb

  • Department of Physics, Bar-Ilan University, Ramat-Gan 52900 Israel

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Issue

Vol. 73, Iss. 1 — January 2006

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