Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

by Michal Fe Kan, Michal Pospi Il, Michal Pospisil, et al.

Poincar -Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincar mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity.

• Format: Hardcover
• Language: English
• ISBN: 012804294X
• ISBN13: 9780128042946
• Release Date: May 2016
• Publisher: Academic Press
• Length: 260 Pages
• Weight: 1.47 lbs.
• Dimensions: 0.6" x 7.5" x 9.3"