Analytical approach to localized structures in a simple reaction-diffusion system

Orazio Descalzi; Yumino Hayase; Helmut R. Brand

doi:10.1103/PhysRevE.69.026121

Analytical approach to localized structures in a simple reaction-diffusion system

Orazio Descalzi^*
, Yumino Hayase
, Helmut R. Brand

^*Autor correspondiente de este trabajo

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

22 Citas (Scopus)

Resumen

We study from an analytical point of view a simple reaction-diffusion model, which admits stable oscillating localized structures as a consequence of the coexistence between a stable limit cycle and a stable fixed point. Using a generalized matching approach we are able to find approximate analytical expressions for localized oscillating structures in this reaction-diffusion model capturing all the essential ingredients of these breathing particlelike solutions.

Idioma original	Inglés
Número de artículo	026121
Páginas (desde-hasta)	026121-1-026121-9
Publicación	Physical Review E
Volumen	69
N.º	2 2
DOI	https://doi.org/10.1103/PhysRevE.69.026121
Estado	Publicada - feb. 2004

Palabras clave

Diffusion
Models, Statistical
Models, Theoretical
Oscillometry
Physical Phenomena
Physics
Systems Theory

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10.1103/PhysRevE.69.026121

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title = "Analytical approach to localized structures in a simple reaction-diffusion system",

abstract = "A simple reaction-diffusion model, which admits stable oscillating localized structures is discussed. The approximate analytical expressions for localized oscillating structures in the reaction-diffusion model are calculated using a generalized matching approach. It is found that the oscillating particlelike solutions lead to the traveling waves generation in the phase because the limit cycle is not a circle. Results show that the analytical approximation captures all the essential ingredients of these breathing particlelike solutions.",

keywords = "Diffusion, Models, Statistical, Models, Theoretical, Oscillometry, Physical Phenomena, Physics, Systems Theory, Diffusion, Models, Statistical, Models, Theoretical, Oscillometry, Physical Phenomena, Physics, Systems Theory",

author = "Orazio Descalzi and Yumino Hayase and Brand, \{Helmut R.\}",

year = "2004",

month = feb,

doi = "10.1103/PhysRevE.69.026121",

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AU - Hayase, Yumino

AU - Brand, Helmut R.

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Y1 - 2004/2

N2 - A simple reaction-diffusion model, which admits stable oscillating localized structures is discussed. The approximate analytical expressions for localized oscillating structures in the reaction-diffusion model are calculated using a generalized matching approach. It is found that the oscillating particlelike solutions lead to the traveling waves generation in the phase because the limit cycle is not a circle. Results show that the analytical approximation captures all the essential ingredients of these breathing particlelike solutions.

AB - A simple reaction-diffusion model, which admits stable oscillating localized structures is discussed. The approximate analytical expressions for localized oscillating structures in the reaction-diffusion model are calculated using a generalized matching approach. It is found that the oscillating particlelike solutions lead to the traveling waves generation in the phase because the limit cycle is not a circle. Results show that the analytical approximation captures all the essential ingredients of these breathing particlelike solutions.

KW - Diffusion

KW - Models, Statistical

KW - Models, Theoretical

KW - Oscillometry

KW - Physical Phenomena

KW - Physics

KW - Systems Theory

KW - Diffusion

KW - Models, Statistical

KW - Models, Theoretical

KW - Oscillometry

KW - Physical Phenomena

KW - Physics

KW - Systems Theory

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DO - 10.1103/PhysRevE.69.026121

M3 - Article

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SN - 1063-651X

VL - 69

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JO - Physical Review E

JF - Physical Review E

IS - 2 2

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ER -

Analytical approach to localized structures in a simple reaction-diffusion system

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