Stable periodic solutions for the hypercycle system |
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| Authors: | J. Hofbauer J. Mallet-Paret H. L. Smith |
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| Affiliation: | (1) Institut für Mathematik, Universität Wien, A-1090 Wien, Austria;(2) Division of Applied Mathematics, Brown University, 02912 Providence, Rhode Island;(3) Department of Mathematics, Arizona State University, 85257 Tempe, Arizona |
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| Abstract: | We consider the hypercycle system of ODEs, which models the concentration of a set of polynucleotides in a flow reactor. Under general conditions, we prove the omega-limit set of any orbit is either an equilibrium or a periodic orbit. The existence of an orbitally asymptotic stable periodic orbit is shown for a broad class of such systems. |
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| Keywords: | Competitive systems cyclic systems hypercycle system monotonicity Poincaré -Bendixson |
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