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Instability of the steady state solution in cell cycle population structure models with feedback

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Abstract

We show that when cell–cell feedback is added to a model of the cell cycle for a large population of cells, then instability of the steady state solution occurs in many cases. We show this in the context of a generic agent-based ODE model. If the feedback is positive, then instability of the steady state solution is proved for all parameter values except for a small set on the boundary of parameter space. For negative feedback we prove instability for half the parameter space. We also show by example that instability in the other half may be proved on a case by case basis.

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Acknowledgements

B.B. acknowledges support from the Grants EP/J013560/1 and OTKA K104745. T.Y. was partially supported by the National Science Foundation Grant 1418787. B.B. and T.Y. thank the staff of the Warwick Mathematics Institute for their hospitality while this paper was written.

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Authors and Affiliations

  1. Mathematics Institute, Warwick University, Coventry, UK

    Balázs Bárány

  2. Department of Stochastics, Budapest University of Technology and Economics, Budapest, Hungary

    Balázs Bárány

  3. Mathematics, Ohio University, Athens, OH, USA

    Gregory Moses & Todd Young

Authors
  1. Balázs Bárány
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  2. Gregory Moses
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  3. Todd Young
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Correspondence to Todd Young.

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Bárány, B., Moses, G. & Young, T. Instability of the steady state solution in cell cycle population structure models with feedback. J. Math. Biol. 78, 1365–1387 (2019). https://doi.org/10.1007/s00285-018-1312-0

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  • DOI: https://doi.org/10.1007/s00285-018-1312-0

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