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Phys. Rev. E 76, 046222 (2007) [6 pages]

Segregation and pursuit waves in activator-inhibitor systems

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Vicenç Méndez1, Werner Horsthemke2, Evgeny P. Zemskov3,4, and José Casas-Vázquez1
1Grup de Física Estadística, Departament de Física, Facultat de Ciències, Edicifi Cc. Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain
2Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA
3Computing Centre of the Russian Academy of Sciences, Vavilova 40, 119991 Moscow, Russia
4Department of Physics and Astronomy, University of New Mexico, 800 Yale Boulevard, Albuquerque, New Mexico 87131, USA

Received 18 July 2006; revised 7 September 2007; published 25 October 2007

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

URL:
http://link.aps.org/doi/10.1103/PhysRevE.76.046222
DOI:
10.1103/PhysRevE.76.046222
PACS:
05.45.−a, 02.50.−r
 
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