Analytical studies of fronts, colonies, and patterns: Combination of the Allee effect and nonlocal competition interactions

M. G. Clerc; D. Escaff; V. M. Kenkre

doi:10.1103/PhysRevE.82.036210

Analytical studies of fronts, colonies, and patterns: Combination of the Allee effect and nonlocal competition interactions

Título traducido de la contribución: Estudios analíticos de frentes, colonias y patrones: Combinación del efecto Allee y las intercciones de competencia no local.

M. G. Clerc, D. Escaff, V. M. Kenkre

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

53 Citas (Scopus)

Resumen

Presentamos un estudio analítico de frentes de viaje, colonias localizadas y patrones extendidos que surgen de una ecuación de reacción-difusión que incorpora simultáneamente dos características: el conocido efecto Allee y las interacciones de competencia espacial no local. El primero es un ingrediente esencial de la mayoría de los sistemas en la dinámica de la población e implica extinción a densidades bajas, crecimiento a densidades más altas y saturación a densidades aún más altas. La última característica también es muy relevante, particularmente para los sistemas biológicos, y va más allá de la suposición poco realista de interacciones de rango cero. Demostramos a través de métodos analíticos exactos que la combinación de las dos características produce una rica diversidad de fenómenos y permite comprender una variedad de cuestiones, incluida la aparición espontánea de colonias.

Título traducido de la contribución	Estudios analíticos de frentes, colonias y patrones: Combinación del efecto Allee y las intercciones de competencia no local.
Idioma original	Inglés
Número de artículo	036210
Publicación	Physical Review E
Volumen	82
N.º	3
DOI	https://doi.org/10.1103/PhysRevE.82.036210
Estado	Publicada - 30 sep. 2010

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title = "Analytical studies of fronts, colonies, and patterns: Combination of the Allee effect and nonlocal competition interactions",

abstract = "We present an analytic study of traveling fronts, localized colonies, and extended patterns arising from a reaction-diffusion equation which incorporates simultaneously two features: the well-known Allee effect and spatially nonlocal competition interactions. The former is an essential ingredient of most systems in population dynamics and involves extinction at low densities, growth at higher densities, and saturation at still higher densities. The latter feature is also highly relevant, particularly to biological systems, and goes beyond the unrealistic assumption of zero-range interactions. We show via exact analytic methods that the combination of the two features yields a rich diversity of phenomena and permits an understanding of a variety of issues including spontaneous appearance of colonies.",

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author = "Clerc, {M. G.} and D. Escaff and Kenkre, {V. M.}",

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N2 - We present an analytic study of traveling fronts, localized colonies, and extended patterns arising from a reaction-diffusion equation which incorporates simultaneously two features: the well-known Allee effect and spatially nonlocal competition interactions. The former is an essential ingredient of most systems in population dynamics and involves extinction at low densities, growth at higher densities, and saturation at still higher densities. The latter feature is also highly relevant, particularly to biological systems, and goes beyond the unrealistic assumption of zero-range interactions. We show via exact analytic methods that the combination of the two features yields a rich diversity of phenomena and permits an understanding of a variety of issues including spontaneous appearance of colonies.

AB - We present an analytic study of traveling fronts, localized colonies, and extended patterns arising from a reaction-diffusion equation which incorporates simultaneously two features: the well-known Allee effect and spatially nonlocal competition interactions. The former is an essential ingredient of most systems in population dynamics and involves extinction at low densities, growth at higher densities, and saturation at still higher densities. The latter feature is also highly relevant, particularly to biological systems, and goes beyond the unrealistic assumption of zero-range interactions. We show via exact analytic methods that the combination of the two features yields a rich diversity of phenomena and permits an understanding of a variety of issues including spontaneous appearance of colonies.

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KW - Linear equations

KW - Analytic method

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KW - Nonlocal

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Analytical studies of fronts, colonies, and patterns: Combination of the Allee effect and nonlocal competition interactions

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