Bifurcation Structures in a Bimodal Piecewise Linear Map

• Main Authors: Anastasiia Panchuk, Iryna Sushko, Viktor Avrutin
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2017-05-01
• Series: Frontiers in Applied Mathematics and Statistics
• Subjects: bimodal piecewise linear map; border collision bifurcation; border collision normal form; degenerate bifurcation; homoclinic bifurcation
• Online Access: http://journal.frontiersin.org/article/10.3389/fams.2017.00007/full

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.