Bifurcation Structures in a Bimodal Piecewise Linear Map

Frontiers in Applied Mathematics and Statistics

Sushko, Iryna¹  Panchuk, Anastasiia¹  Avrutin, Viktor² 

[1] Department of Differential Equations and Oscillation Theory, Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;Instituts für Systemtheorie und Regelungstechnik (IST), University of Stuttgart, Stuttgart, Germany

关键词: Bimodal piecewise linear map;    Border collision bifurcation;    border collision normal form;    Degenerate bifurcation;    Homoclinic bifurcation;   

DOI  :  10.3389/fams.2017.00007

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY