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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we address the stability of transport systems and wavepropagation on networks with time-varying parameters. We do so by reformulatingthese systems as non-autonomous difference equations and by providing asuitable representation of their solutions in terms of their initial conditionsand some time-dependent matrix coefficients. This enables us to characterizethe asymptotic behavior of solutions in terms of such coefficients. In the caseof difference equations with arbitrary switching, we obtain a delay-independentgeneralization of the well-known criterion for autonomous systems due to Haleand Silkowski. As a consequence, we show that exponential stability oftransport systems and wave propagation on networks is robust with respect tovariations of the lengths of the edges of the network preserving their rationaldependence structure. This leads to our main result: the wave equation on anetwork with arbitrarily switching damping at external vertices isexponentially stable if and only if the network is a tree and the damping isbounded away from zero at all external vertices but at most one.

Stability of non-autonomous difference equations with applications to transport and wave propagation on networks