Segregation and pursuit waves in activator-inhibitor systems

Vicenç Méndez; Werner Horsthemke; Evgeny P. Zemskov; José Casas-Vázquez

doi:10.1103/PhysRevE.76.046222

Segregation and pursuit waves in activator-inhibitor systems

Vicenç Méndez, Werner Horsthemke, Evgeny P. Zemskov, José Casas-Vázquez

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Resum

We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison with the corresponding Rinzel-Keller model for the usually studied case of self-diffusion is performed. © 2007 The American Physical Society.

Idioma original	Anglès
Número d’article	046222
Revista	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volum	76
DOIs	https://doi.org/10.1103/PhysRevE.76.046222
Estat de la publicació	Publicada - 25 d’oct. 2007

Accés al document

10.1103/PhysRevE.76.046222

https://ddd.uab.cat/record/118212

Com citar-ho

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title = "Segregation and pursuit waves in activator-inhibitor systems",

abstract = "We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison with the corresponding Rinzel-Keller model for the usually studied case of self-diffusion is performed. {\textcopyright} 2007 The American Physical Society.",

author = "Vicen{\c c} M{\'e}ndez and Werner Horsthemke and Zemskov, {Evgeny P.} and Jos{\'e} Casas-V{\'a}zquez",

year = "2007",

month = oct,

day = "25",

doi = "10.1103/PhysRevE.76.046222",

language = "English",

volume = "76",

journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",

issn = "1539-3755",

publisher = "American Physical Society",

}

TY - JOUR

T1 - Segregation and pursuit waves in activator-inhibitor systems

AU - Méndez, Vicenç

AU - Horsthemke, Werner

AU - Zemskov, Evgeny P.

AU - Casas-Vázquez, José

PY - 2007/10/25

Y1 - 2007/10/25

N2 - We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison with the corresponding Rinzel-Keller model for the usually studied case of self-diffusion is performed. © 2007 The American Physical Society.

AB - We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison with the corresponding Rinzel-Keller model for the usually studied case of self-diffusion is performed. © 2007 The American Physical Society.

U2 - 10.1103/PhysRevE.76.046222

DO - 10.1103/PhysRevE.76.046222

M3 - Article

SN - 1539-3755

VL - 76

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

M1 - 046222

ER -

Segregation and pursuit waves in activator-inhibitor systems

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