Symmetry properties and bifurcation analysis of a class of periodically forced chemical reactors |
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Authors: | Lucia RussoErasmo Mancusi Pier Luca MaffettoneSilvestro Crescitelli |
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Affiliation: | a Dipartimento d'Ingegneria Chimica Università “Federico II”, Piazzale Tecchio 80, I-80125, Napoli, Italy b Facoltà di Ingegneria, Università del Sannio, Piazza Roma, 82100, Benevento, Italy c Dipartimento di Scienza dei Materiali ed Ingegneria Chimica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129, Torino, Italy |
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Abstract: | In this work, we discuss how periodic forcing may induce symmetry properties into mathematical models of chemical reactors. We define a class of reactors subjected to discontinuous periodic forcing, and show that all the reactors belonging to this class have spatio-temporal symmetry. This symmetry and its influence on the possible bifurcation scenarios are discussed. The bifurcation analysis is carried out with suitable discrete systems that exploit a property of the Poincaré map. In fact, it is shown that the spatio-temporal symmetry induced by the forcing makes the Poincaré map of the continuous system an iterate of another map. On this basis, a technique to implement parameter continuation methods is proposed. With such a technique, it is also possible to characterize symmetric and nonsymmetric regimes and unstable limit sets otherwise undetected with “bruteforce” approaches. Examples for reverseflow reactors and networks of n-reactors with periodically switched feed and discharge positions are presented. |
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Keywords: | Periodically forced chemical reactors Symmetric dynamical systems Symmetry breaking bifurcations Parameter continuation |
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