1998/12/21 by Mads Ipsen, M. Ipsen, F. Hynne +5
Computer Science · Medicine · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #chao-dyn #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9812028
33 pages, 7 figures, and 7 tables. Submitted to Physica-D. (please send email to [email protected] to retrieve postscript file with color graphics) Please address any correspondence by email to [email protected]
arxiv created 1998/12/21 · openalex publication_date 1998/12/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.