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The Dynamics of Catalytic Hypercycles — A Stochastic Simulation

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Stochastic Phenomena and Chaotic Behaviour in Complex Systems

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 21))

Abstract

A stochastic simulation of elementary hypercycles of dimensions n = 3, 4, 5 and 8 is presented. In populations of sizes which can be realized in nature and in laboratory experiments, hypercycles with dimensions n ≥ 5 die out after a short time. This instability of hypercycles of higher dimensions is to be distinguished from a general instability of the model system presented: all model systems considered here are metastable in the sense that the system dies out with probability one for infinite time.

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References

  1. J. Hofbauer, P. Schuster: “Dynamics of Linear and Nonlinear Autocatalysis and Competition”, this volume.

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  2. M. Eigen, P. Schuster: “The Hypercycle-A Principle of Natural SelfOrganization” ( Springer, Berlin 1979 )

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  3. K. Sigmund, P. Schuster: “Permanence and Univadability for Deterministic Population Models”, this volume.

    Google Scholar 

  4. P. Schuster, K. Sigmund, R. Wolff: J.Math.Analysis and Applications 78, 88 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Schuster, K. Sigmund, R. Wolff: Bull.Math.Biol. 40, 743 (1978)

    MathSciNet  Google Scholar 

  6. P. Phillipson, P. Schuster: J.Chem.Phys. 79, 3807 (1983)

    Article  ADS  Google Scholar 

  7. D. A. McQuarrie: J.Appl.Prob. 4, 413 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  8. C. W. Gardiner, S. Chaturvedi: J.Stat.Phys. 17, 429 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  9. N. G. van Kampen: “Stochastic Processes in Physics and Chemistry” ( North-Holland, Amsterdam 1981 )

    MATH  Google Scholar 

  10. D. T. Gillespie: J.Phys.Chem. 81, 2340 (1977)

    Article  Google Scholar 

  11. D. T. Gillespie: J.Compt.Phys. 22, 403 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  12. P. E. Phillipson, P. Schuster, F. Kemler: “Dynamical Machinery of a Biochemical Clock” (Bull.Math.Biol., in press)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, Stuttgart 80, D-7000, Fed. Rep. of Germany

    A. M. Rodriguez-Vargas & P. Schuster

  2. Institut für Theoretische Chemie und Strahlenchemie, Universität Wien, Währinger Straße 17, Wien, A-1090, Austria

    A. M. Rodriguez-Vargas & P. Schuster

  3. Departamento de Fisica, Universidad de los Andes, Bogota, D. E., Columbia

    A. M. Rodriguez-Vargas

Authors
  1. A. M. Rodriguez-Vargas
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  2. P. Schuster
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Editor information

Editors and Affiliations

  1. Institut für Theoretische Chemie und Strahlenchemie, Universität Wien, Währinger Straße 17, Wien, A-1090, Austria

    Peter Schuster

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© 1984 Springer-Verlag Berlin Heidelberg

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Rodriguez-Vargas, A.M., Schuster, P. (1984). The Dynamics of Catalytic Hypercycles — A Stochastic Simulation. In: Schuster, P. (eds) Stochastic Phenomena and Chaotic Behaviour in Complex Systems. Springer Series in Synergetics, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69591-9_18

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  • DOI: https://doi.org/10.1007/978-3-642-69591-9_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69593-3

  • Online ISBN: 978-3-642-69591-9

  • eBook Packages: Springer Book Archive

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