AUTHOR=Panchuk Anastasiia , Sushko Iryna , Avrutin Viktor 

TITLE=Bifurcation Structures in a Bimodal Piecewise Linear Map

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=3

YEAR=2017

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2017.00007

DOI=10.3389/fams.2017.00007

ISSN=2297-4687

ABSTRACT=<p>In this paper we present an overview of the results concerning dynamics of a piecewise linear bimodal map. The organizing principles of the bifurcation structures in both regular and chaotic domains of the parameter space of the map are discussed. In addition to the previously reported structures, a family of regions closely related to the so-called U-sequence is described. The boundaries of distinct regions belonging to these structures are obtained analytically using the skew tent map and the map replacement technique.</p>