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

This paper is concerned with the existence of multiple stable fixed pointsolutions of the homogeneous Kuramoto model. We develop a necessary conditionfor the existence of stable fixed points for the general network Kuramotomodel. This condition is applied to show that for sufficiently dense n-nodenetworks, with node degrees at least 0.9395(n-1), the homogeneous (equalfrequencies) model has no non-zero stable fixed point solution over the fullspace of phase angles in the range -Pi to Pi. This result together withexisting research proves a conjecture of Verwoerd and Mason (2007) that for thecomplete network and homogeneous model the zero fixed point has a basin ofattraction consisting of the entire space minus a set of measure zero. Thenecessary conditions are also tested to see how close to sufficiency they mightbe by applying them to a class of regular degree networks studied by Wiley,Strogatz and Girvan (2006).

There are no non-zero Stable Fixed Points for dense networks in the homogeneous Kuramoto model