Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

Feckan, Michal; Pospí?il, Michal

ISBN 10: 012804294X / ISBN 13: 9780128042946

Verlag: Academic Press, 2016

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Bibliografische Details

• Titel: Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems
• Verlag: Academic Press
• Erscheinungsjahr: 2016
• Sprache: Englisch
• ISBN-10: 012804294X
• ISBN-13: 9780128042946
• Einband: Hardcover
• Zustand: New

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Inhaltsangabe

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.

Über die Autorinnen und Autoren

Professor Michal Fečkan works at the Department of Mathematical Analysis and Numerical Mathematics at the Faculty of Mathematics, Physics, and Informatics at Comenius University. He specializes in nonlinear functional analysis, and dynamic systems and their applications. There is much interest in his contribution to the analysis of solutions of equations with fractional derivatives. Fečkan has written several scientific monographs that have been published at top international publishing houses

Michal Pospíšil is senior researcher at the Mathematical Institute of Slovak Academy of Sciences in Bratislava, Slovak Republic. He obtained his Ph.D. (applied mathematics) from the Mathematical Institute of Slovak Academy of Sciences in Bratislava, Slovak Republic. He is interested in discontinuous dynamical systems and delayed differential equations.