Jones, A.E. and Nisbet, R.M. and Gurney, William and Blythe, S.P.
(1988)
*Period to delay ratios near stability boundaries for systems with delayed feedback.*
Journal of Mathematical Analysis and Applications, 135 (1).
pp. 354-368.
ISSN 0022-247X

## Abstract

We show how, with a suitable choice of a “free” parameter, period to delay ratios near stability boundaries may be found for delay-differential systems with a single delay, and with a characteristic equation of the form F(λ) + G(λ)e−λτ = 0. When F and G do not depend on the delay, τ itself is a natural choice for the free parameter, and the the period to delay ratio can be easily found for given values of the parameters of F and G. It is shown that if more than one stability switch occurs for such a system as τ is increased, then the period to delay ratio will become progressively smaller with each stable-unstable change. By considering a model with a variable delay, we demonstrate how to determine period to delay ratios when the characteristic equation is such that F and G themselves depend on τ, and show that for the model considered, the period must always lie between τ and 2τ. An Appendix considers the appearance of zero eigenvalues in such characteristic equations.

Item type: | Article |
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ID code: | 41683 |

Keywords: | stability boundaries, delay ratio, Probabilities. Mathematical statistics, Analysis, Applied Mathematics |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date Deposited: | 24 Oct 2012 10:59 |

Last modified: | 21 May 2015 15:03 |

URI: | http://strathprints.strath.ac.uk/id/eprint/41683 |

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