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| Limit Cycles in a Two-Species Reaction |
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| KeyWord:Limit cycles two-species reaction third order reaction step |
| Author Name | Affiliation | | Brigita Ferčec | Faculty of Energy Technology, Hočevarjev trg 1, 8270 Krško, Slovenia
Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia | | Ilona Nagy | Department of Mathematical Analysis, Budapest University of Technology and Economics, Egry J. u. 1., H-1111 Budapest, Hungary | | Valery G. Romanovski | Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia
Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška c. 46, 2000 Maribor, Slovenia
Faculty of Natural Science and Mathematics, University of Maribor, Koroška c. 160, 2000 Maribor, Slovenia | | Gábor Szederkényi | Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/A. H-1083 Budapest, Hungary | | János Tóth | Department of Mathematical Analysis, Budapest University of Technology and Economics, Egry J. u. 1., H-1111 Budapest, Hungary
Laboratory for Chemical Kinetics, Eötvös Loránd University, Pázmány P.sétány 1/A, H-1117 Budapest, Hungary |
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| Abstract: |
| Kinetic differential equations, being nonlinear, are capable of producing many kinds of exotic phenomena. However, the existence of multistationarity, oscillation or chaos is usually proved by numerical methods. Here we investigate a relatively simple reaction among two species consisting of five reaction steps, one of the third order. Using symbolic methods we find the necessary and sufficient conditions on the parameters of the kinetic differential equation of the reaction under which a limit cycle bifurcates from the stationary point in the positive quadrant in a supercritical Hopf bifurcation. We also performed the search for partial integrals of the system and have found one such integral. Application of the methods needs computer help (Wolfram language and the Singular computer algebra system) because the symbolic calculations to carry out are too complicated to do by hand. |
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