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Phys. Rev. E 52, 129 - 136 (1995)

Global stability of stationary patterns in bistable reaction-diffusion systems

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G. Izús, R. Deza, and O. Ramírez
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600 Mar del Plata, Argentina

Horacio S. Wio and D. H. Zanette
Centro Atómico Bariloche, Comisión Nacional de Energía Atómica and Instituto Balseiro, Universidad Nacional de Cuyo, 8400 San Carlos de Bariloche, Argentina

C. Borzi
Comisión Nacional de Energía Atómica, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina

Received 1 December 1994

We study a piecewise linear version of a one-component, one-dimensional reaction-diffusion bistable model, with the aim of analyzing the effect of boundary conditions on the formation and stability of stationary patterns. The analysis proceeds through the study of the behavior of the Lyapunov functional in terms of a control parameter: the reflectivity at the boundary. We show that, in this example, this functional has a very simple and direct geometrical interpretation.


©1995 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevE.52.129
DOI: 10.1103/PhysRevE.52.129
PACS: 05.70.Ln, 47.54.+r, 82.40.Ck

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