Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures

The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.

Product details

• Authors: Viktor Avrutin, Avrutin Viktor, Laura Gardini, Gardini Laura, Iryna Sushko, Laura Gardini, Michael Schanz, Irina Sushko, Sushko Iryna, Fabio Tramontana, Viktor Avrutin, Laura Gardini Iryna Sus Viktor Avrutin
• Publisher: Ingram Publishers Services
• Languages: English
• Product format: Hardback
• Released: 31.08.2019
• EAN: 9789814368827
• ISBN: 978-981-4368-82-7
• Series: World Scientific Series on Non; World Scientific Series on Nonlinear Science Series A; World Scientific Series on Non
• Subjects: Natural sciences, medicine, IT, technology > IT, data processing > Programming languages; MATHEMATICS / Linear & Nonlinear Programming, Discontinuous Maps; Piecewise-Smooth Maps; Piecewise-Linear Maps, Nonlinear science