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

We study homoclinic bifurcations in an interval map associated with asaddle-focus of (2, 1)-type in $\mathbb{Z}_2$-symmetric systems. Our study ofthis map reveals the homoclinic structure of the saddle-focus, with abifurcation unfolding guided by the codimension-two Belyakov bifurcation. Weconsider three parameters of the map, corresponding to the saddle quantity,splitting parameter, and focal frequency of the smooth saddle-focus in aneighborhood of homoclinic bifurcations. We symbolically encode dynamics of themap in order to find stability windows and locate homoclinic bifurcation setsin a computationally efficient manner. The organization and possible shapes ofhomoclinic bifurcation curves in the parameter space are examined, taking intoaccount the symmetry and discontinuity of the map. Sufficient conditions forstability and local symbolic constancy of the map are presented. This studyfurnishes insights into the structure of homoclinic bifurcations of thesaddle-focus map, furthering comprehension of low-dimensional chaotic systems.

Bifurcation structure of interval maps with orbits homoclinic to a saddle-focus