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/

Zendy Plus

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

Zendy Tools

Zendy Open

We investigate the global dynamics from a measure-theoretic perspective forsmooth flows with invariant cones of rank k. For such systems, it is shown thatprevalent (or equivalently, almost all) orbits will be pseudo-ordered orconvergent to equilibria. This reduces to Hirsch's prevalent convergenceTheorem if the rank k=1; and implies an almost-sure Poincare-Bendixson Theoremfor the case k=2. These results are then applied to obtain an almost surePoincare-Bendixson theorem for high-dimensional differential equations.

Prevalent behavior and almost sure Poincare-Bendixson Theorem for smooth flows with invariant k-cones