location:  Publications → journals → CMB
Abstract view

# Stability Threshold for Scalar Linear Periodic Delay Differential Equations

Published:2016-09-14
Printed: Dec 2016
• Kyeongah Nah,
Bolyai Institute, University of Szeged, Szeged H-6720, Aradi vértanúk tere 1., Hungary
• Gergely Röst,
Bolyai Institute, University of Szeged, Szeged H-6720, Aradi vértanúk tere 1., Hungary
 Format: LaTeX MathJax PDF

## Abstract

We prove that for the linear scalar delay differential equation $$\dot{x}(t) = - a(t)x(t) + b(t)x(t-1)$$ with non-negative periodic coefficients of period $P\gt 0$, the stability threshold for the trivial solution is $r:=\int_{0}^{P} \left(b(t)-a(t) \right)\mathrm{d}t=0,$ assuming that $b(t+1)-a(t)$ does not change its sign. By constructing a class of explicit examples, we show the counter-intuitive result that in general, $r=0$ is not a stability threshold.
 Keywords: delay differential equation, stability, periodic system
 MSC Classifications: 34K20 - Stability theory 34K06 - Linear functional-differential equations

 top of page | contact us | privacy | site map |