Poincaré-andronov-melnikov Analysis for Non-smooth Systems - Rilegato

Feckan, Michal; Pospí il, Michal

Rilegato

ISBN 10: 012804294X ISBN 13: 9780128042946

Casa editrice: Academic Pr, 2016

Riassunto

Poincaré-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 Poincaré 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.

• Extends Melnikov analysis of the classic Poincaré and Andronov staples, pointing to a general theory for freedom in dimensions of spatial variables and parameters as well as asymptotical results such as stability, instability, and hyperbolicity
• Presents a toolbox of critical theoretical techniques for many practical examples and models, including non-smooth dynamical systems
• Provides realistic models based on unsolved discontinuous problems from the literature and describes how Poincaré-Andronov-Melnikov analysis can be used to solve them
• Investigates the relationship between non-smooth systems and their continuous approximations

Su questo libro

Informazioni sull?autore

Michal Feckan is Professor of Mathematics at the Department of Mathematical Analysis and Numerical Mathematics on the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovak Republic. He obtained his Ph.D. (mathematics) from the Mathematical Institute of Slovak Academy of Sciences in Bratislava, Slovak Republic. He is interested in nonlinear functional analysis, bifurcation theory and dynamical systems with applications to mechanics and vibrations.

Dettagli dell?edizione

• Editore: Academic Pr
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 012804294X
• ISBN 13: 9780128042946
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 260
• Contatto del produttore: non disponibile