Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems
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Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems


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About the Book

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.

Table of Contents:
An introductory example I. Piecewise-smooth systems of forced ODEs I.2. Bifurcation from family of periodic orbits in autonomous systems I.3. Bifurcation from single periodic orbit in autonomous systems I.4. Sliding solution of periodically perturbed systems I.5. Weakly coupled oscillators Reference II. Forced hybrid systems II.1. Periodically forced impact systems II.2. Bifurcation from family of periodic orbits in forced billiards Reference III. Continuous approximations of non-smooth systems III.1. Transversal periodic orbits III.2. Sliding periodic orbits III.3. Impact periodic orbits III.4. Approximation and dynamics Reference Appendix

About the Author :
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.


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Product Details
  • ISBN-13: 9780128042946
  • Publisher: Elsevier Science Publishing Co Inc
  • Publisher Imprint: Academic Press Inc
  • Height: 235 mm
  • No of Pages: 260
  • Width: 191 mm
  • ISBN-10: 012804294X
  • Publisher Date: 17 May 2016
  • Binding: Hardback
  • Language: English
  • Weight: 716 gr


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