Abstract
It is now well documented that, despite their complexity, the dynamics of physicochemical systems driven away from thermal equilibrium may be reduced, close to bifurcation points, to much simpler forms describing the universal properties of the spatio-temporal patterns. One of the most celebrated instabilities in this framework corresponds to the Hopf bifurcation that induces oscillations of the limit cycle type, which are of particular interest in nonlinear chemical systems, nonlinear optics and biology. The description of real oscillatory media is based on a combination of generic aspects that depend only on the characteristics of the bifurcation and of the symmetries of the problem and of nongeneric aspects that arise through experimental set-ups, boundary or geometrical effects, and so forth. Hence, it is interesting to discuss both aspects with the simplest description of oscillatory media close to a supercritical Hopf bifurcation, namely the complex Ginzburg-Landau equation.
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Walgraef, D. (1997). The Hopf Bifurcation and Related Spatio-Temporal Patterns. In: Spatio-Temporal Pattern Formation. Partially Ordered Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1850-0_5
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DOI: https://doi.org/10.1007/978-1-4612-1850-0_5
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