English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In our adjacent work, we developed a spectral comparison principle forcompound cocycles generated by delay equations. In particular, this principleallows to derive frequency conditions (inequalities) for the uniformexponential stability of such cocycles by means of their comparison withstationary problems. Such inequalities are hard to verify analytically sincethey contain resolvents of additive compound operators and to compute theresolvents it is required solving a first-order PDEs with boundary conditionsinvolving both partial derivatives and delays.  In this work, we develop approximation schemes to verify some of the arisingfrequency inequalities. Beside some general results, we mainly stick to thecase of scalar equations. By means of the Suarez-Schopf delayed oscillator andthe Mackey-Glass equations, we demonstrate applications of the theory to revealregions in the space of parameters where the absence of closed invariantcontours can be guaranteed. Since our conditions are robust, so close systemsalso satisfy them, we expect them to actually imply the global stability, as inknown finite-dimensional results utilizing variants of the Closing Lemma whichis still awaiting developments in infinite dimensions.

Frequency conditions for the global stability of nonlinear delay equations with several equilibria