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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

At a border-collision bifurcation a fixed point of a piecewise-smooth mapintersects a surface where the functional form of the map changes. Near ageneric border-collision bifurcation there are two fixed points, each of whichexists on one side of the bifurcation. A simple eigenvalue condition indicateswhether the fixed points exist on different sides of the bifurcation (this casecan be interpreted as the persistence of a single fixed point), or on the sameside of the bifurcation (in which case the bifurcation is akin to a saddle-nodebifurcation). A similar eigenvalue condition indicates whether or not thereexists a period-two solution on one side of the bifurcation. Previously theseconditions have been combined to obtain five distinct scenarios for theexistence and relative coexistence of fixed points and period-two solutionsnear border-collision bifurcations. In this Letter, it is shown that one ofthese scenarios, namely that two fixed points exist on one side of thebifurcation and a period-two solution exists on the other side of thebifurcation, cannot occur. The remaining four scenarios are feasible. Thereforethere are exactly four distinct scenarios for fixed points and period-twosolutions near border-collision bifurcations.

On the relative coexistence of fixed points and period-two solutions near border-collision bifurcations