You, Yuncheng; Zhou, Shengfan Global dissipative dynamics of the extended Brusselator system. (English) Zbl 1253.35192 Nonlinear Anal., Real World Appl. 13, No. 6, 2767-2789 (2012). Summary: The existence of a global attractor for the solution semiflow of the extended Brusselator system in the \(L^{2}\) phase space is proved, which is a cubic-autocatalytic and partially reversible reaction-diffusion system with linear coupling between two compartments. The method of grouping and rescaling estimation is developed to deal with the challenge in proving the absorbing property and the asymptotic compactness of this typical multi-component reaction-diffusion system. The regularity and the finite dimensionality of the global attractor are also studied. The results and methodology can find many applications and further extensions in investigations of complex biological and biochemical dynamical systems. Cited in 7 Documents MSC: 35Q92 PDEs in connection with biology, chemistry and other natural sciences 35K57 Reaction-diffusion equations 35B65 Smoothness and regularity of solutions to PDEs Keywords:Brusselator system; dissipative dynamics; global attractor; absorbing set; asymptotic compactness; fractal dimension PDFBibTeX XMLCite \textit{Y. You} and \textit{S. Zhou}, Nonlinear Anal., Real World Appl. 13, No. 6, 2767--2789 (2012; Zbl 1253.35192) Full Text: DOI arXiv References: [1] Prigogine, I.; Lefever, R., Symmetry-breaking instabilities in dissipative systems, J. Chem. Phys., 48, 1665-1700 (1968) [2] Ashkenazi, M.; Othmer, H. G., Spatial patterns in coupled biochemical oscillators, J. Math. Biol., 5, 305-350 (1978) · Zbl 0381.92006 [3] Brown, K. J.; Davidson, F. A., Global bifurcation in the Brusselator system, Nonlinear Anal., 24, 1713-1725 (1995) · Zbl 0829.35010 [4] Lee, K. J.; McCormick, W. 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