Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 354-368 |
| Number of pages | 15 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 135 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Oct 1988 |
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Keywords
- stability boundaries
- delay ratio
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Period to delay ratios near stability boundaries for systems with delayed feedback. / Jones, A.E.; Nisbet, R.M.; Gurney, William; Blythe, S.P.
In: Journal of Mathematical Analysis and Applications, Vol. 135, No. 1, 10.1988, p. 354-368.Research output: Contribution to journal › Article
TY - JOUR
T1 - Period to delay ratios near stability boundaries for systems with delayed feedback
AU - Jones, A.E.
AU - Nisbet, R.M.
AU - Gurney, William
AU - Blythe, S.P.
PY - 1988/10
Y1 - 1988/10
N2 - 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.
AB - 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.
KW - stability boundaries
KW - delay ratio
U2 - 10.1016/0022-247X(88)90160-6
DO - 10.1016/0022-247X(88)90160-6
M3 - Article
VL - 135
SP - 354
EP - 368
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -