Amplitude Equations for Reaction-Diffusion Systems with a Hopf Bifurcation and Slow Real Modes

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Using a normal form approach described in a previous paper we derive an amplitude equation for a reaction-diffusion system with a Hopf bifurcation coupled to one or more slow real eigenmodes. The new equation is useful even for systems where the actual bifurcation underlying the description cannot be realized, which is typical of chemical systems. For a fold-Hopf bifurcation, the equation successfully handles actual chemical reactions where the complex Ginzburg-Landau equation fails. For a realistic chemical model of the Belousov-Zhabotinsky reaction, we compare solutions to the reaction-diffusion equation with the approximations by the complex Ginzburg-Landau equation and the new distributed fold-Hopf equation.
33 pages, 7 figures, and 7 tables. Submitted to Physica-D. (please send email to mads.ipsen@uni-c.dk to retrieve postscript file with color graphics) Please address any correspondence by email to mads.ipsen@uni-c.dk

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Chaotic Dynamics

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http://salesiana.dossiersoluciones.com/handle/123456789/15672

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/chao-dyn/9812028
 http://arxiv.org/abs/chao-dyn/9812028

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arXiv