Exponential decay for negative feedback loop with distributed delay

Jan Haskovec

doi:10.1016/j.aml.2020.106419

Exponential decay for negative feedback loop with distributed delay

Jan Haskovec

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses elementary tools of calculus and is robust towards possible extensions to more complex settings, in particular, systems of delay differential equations. We illustrate the applicability of the method to particular distributions — Dirac delta, Gamma distribution, uniform and truncated normal distributions.

Original language	English (US)
Pages (from-to)	106419
Journal	Applied Mathematics Letters
Volume	107
DOIs	https://doi.org/10.1016/j.aml.2020.106419
State	Published - Apr 24 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: JH acknowledges the support of the KAUST baseline funds. This work was done partially while the author was visiting the Institute for Mathematical Sciences, National University of Singapore in 2019. The visit was supported by the Institute.

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10.1016/j.aml.2020.106419

https://repository.kaust.edu.sa/bitstream/10754/662736/1/Haskovec-AML.pdf

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abstract = "We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses elementary tools of calculus and is robust towards possible extensions to more complex settings, in particular, systems of delay differential equations. We illustrate the applicability of the method to particular distributions — Dirac delta, Gamma distribution, uniform and truncated normal distributions.",

author = "Jan Haskovec",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: JH acknowledges the support of the KAUST baseline funds. This work was done partially while the author was visiting the Institute for Mathematical Sciences, National University of Singapore in 2019. The visit was supported by the Institute.",

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N2 - We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses elementary tools of calculus and is robust towards possible extensions to more complex settings, in particular, systems of delay differential equations. We illustrate the applicability of the method to particular distributions — Dirac delta, Gamma distribution, uniform and truncated normal distributions.

AB - We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses elementary tools of calculus and is robust towards possible extensions to more complex settings, in particular, systems of delay differential equations. We illustrate the applicability of the method to particular distributions — Dirac delta, Gamma distribution, uniform and truncated normal distributions.

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JF - Applied Mathematics Letters

ER -

Exponential decay for negative feedback loop with distributed delay

Abstract

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