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Global dynamics of the smallest chemical reaction system with Hopf bifurcation

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Abstract

The global behavior of solutions is described for the smallest chemical reaction system that exhibits a Hopf bifurcation, discovered in [12]. This three-dimensional system is a competitive system and a monotone cyclic feedback system. The Poincaré–Bendixson theory extends to such systems [2,3,6,8] and a Bendixson criterion exists to rule out periodic orbits [4].

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA

    Hal L. Smith

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  1. Hal L. Smith
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Correspondence to Hal L. Smith.

Additional information

Hal L. Smith is supported by NSF Grant DMS-0918440.

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Smith, H.L. Global dynamics of the smallest chemical reaction system with Hopf bifurcation. J Math Chem 50, 989–995 (2012). https://doi.org/10.1007/s10910-011-9946-9

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  • DOI: https://doi.org/10.1007/s10910-011-9946-9

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