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On Stability of Limit Cycles of a Prototype Problem of Piecewise Linear Systems

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Emergent Problems in Nonlinear Systems and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 393))

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Summary

The purpose of this paper is to develop a machinery to analyze existence and stability of limit cycle of a prototype of piecewise linear systems, possibly with delays in switching rules. The study of this type of problems is motivated by modelling cell cycle regulation. The results are applied to a cell cycle model of fission yeast. It is shown that the cell cycle model has a limit cycle and it is stable and criterion of the stability regions are also given.

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References

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Authors and Affiliations

  1. Dept. of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden and The Computational Medicine group, Center for Molecular Medicine, Department of Medicine, Karolinska Institutet, Karolinska University Hospital, Solna, SE-171 76 Stockholm, Sweden

    O. Eriksson

  2. The Computational Medicine group, Center for Molecular Medicine, Department of Medicine, Karolinska Institutet, Karolinska University Hospital, Solna, SE-171 76 Stockholm, Sweden and Division of Computational Biology, Department of Physics, Chemistry and Biology, The Institute of Technology, Linköping University, SE-581 83 Linköping, Sweden

    J. Tègner

  3. Department of Mathematics, Stockholm University, SE-10691, Stockholm, Sweden

    Y. Zhou

Authors
  1. O. Eriksson
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  2. J. Tègner
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  3. Y. Zhou
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Statistics, Center for BioCybernetics and Intelligent Systems, Texas Tech University, Broadway and Boston, 79409-1042, Lubbock, TX, USA

    Bijoy K. Ghosh

  2. Dept. of Mathematics and Statistics, Texas Tech University, Broadway and Boston, 79409-1042, Lubbock, TX, USA

    Clyde F. Martin

  3. Dept. of Mathematics, Stockholm University, SE-106 91, Stockholm, Sweden

    Yishao Zhou

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© 2009 Springer-Verlag Berlin Heidelberg

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Eriksson, O., Tègner, J., Zhou, Y. (2009). On Stability of Limit Cycles of a Prototype Problem of Piecewise Linear Systems. In: Ghosh, B.K., Martin, C.F., Zhou, Y. (eds) Emergent Problems in Nonlinear Systems and Control. Lecture Notes in Control and Information Sciences, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03627-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-03627-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03626-2

  • Online ISBN: 978-3-642-03627-9

  • eBook Packages: EngineeringEngineering (R0)

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