Chapter

Emergent Problems in Nonlinear Systems and Control

Volume 393 of the series Lecture Notes in Control and Information Sciences pp 43-55

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

  • O. ErikssonAffiliated withDept. 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
  • , J. TègnerAffiliated withThe 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
  • , Y. ZhouAffiliated withDepartment of Mathematics, Stockholm University

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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.