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On the origin of chaos in the Belousov-Zhabotinsky reaction in closed and unstirred reactors. (English) Zbl 1213.37082

Summary: We investigate the origin of deterministic chaos in the Belousov-Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator-diffusion system to the Navier-Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations and spatial-temporal dynamics. In particular, numerical solutions to the corresponding reaction-diffusion-convection (RDC) problem show that natural convection can change the evolution of the concentration distribution as well as oscillation patterns. The results suggest a new way of perceiving the BZ reaction when it is conducted in CURs. In conflict with the common experience, chemical oscillations are no longer a mere chemical process. Within this framework the evolution of all dynamical observables are demonstrated to converge to the regime imposed by the RDC coupling: chemical and spatial-temporal chaos are genuine manifestations of the same phenomenon.

MSC:

37G35 Dynamical aspects of attractors and their bifurcations
35B36 Pattern formations in context of PDEs
35Q35 PDEs in connection with fluid mechanics
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