The Saddle-Node of Nearly Homogeneous Wave Trains in Reaction–Diffusion Systems |
| |
Authors: | Jens D M Rademacher Arnd Scheel |
| |
Institution: | (1) Centrum voor Wiskunde en Informatica (CWI), Kruislaan 413, 1098 SJ Amsterdam, The Netherlands;(2) School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN 55455, USA |
| |
Abstract: | We study the saddle-node bifurcation of a spatially homogeneous oscillation in a reaction-diffusion system posed on the real
line. Beyond the stability of the primary homogeneous oscillations created in the bifurcation, we investigate existence and
stability of wave trains with large wavelength that accompany the homogeneous oscillation. We find two different scenarios
of possible bifurcation diagrams which we refer to as elliptic and hyperbolic. In both cases, we find all bifurcating wave
trains and determine their stability on the unbounded real line. We confirm that the accompanying wave trains undergo a saddle-node
bifurcation parallel to the saddle-node of the homogeneous oscillation, and we also show that the wave trains necessarily
undergo sideband instabilities prior to the saddle-node. |
| |
Keywords: | Saddle-node bifurcation wave trains homogeneous oscillation stability reaction diffusion systems |
本文献已被 SpringerLink 等数据库收录! |
|