caa a22 4500 38810886X CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500031073 doi S0308210500031073 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500031073 Rubin J. E. Division of Applied Mathematics Brown University Box F, Providence, RI 02912, USA Stability, bifurcations and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system [Elektronische Daten] [J. E. Rubin] We consider a class of inhomogeneous systems of reaction-diffusion equations that includes a model for cavity dynamics in the semiconductor Fabry-Pérot interferometer. By adapting topological and geometrical methods, we prove that a standing pulse solution to this system is stable in a certain parameter regime, under the simplification of homogeneous illumination. Moreover, we explain two bifurcation mechanisms which can cause a loss of stability, yielding travelling and standing pulses, respectively. We compute conditions for these bifurcations to persist when inhomogeneity is restored through a certain general perturbation. Under certain of these conditions, a Hopf bifurcation results, producing periodic solutions called edge oscillations. These inhomogeneous bifurcation mechanisms represent new means for the generation of solutions displaying edge oscillations in a reaction-diffusion system. The oscillations produced by each inhomogeneous bifurcation are expected to depend qualitatively on the properties of the corresponding homogeneous bifurcation. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/5(1999), 1033-1079 0308-2105 129:5<1033 1999 129 PRM https://doi.org/10.1017/S0308210500031073 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500031073 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rubin J. E. Division of Applied Mathematics Brown University Box F, Providence, RI 02912, USA NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/5(1999), 1033-1079 0308-2105 129:5<1033 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge