Описание: This book presents the basis of Poincare plot and focus especially on traditional and new methods for analysing the geometry, temporal and spatial dynamics disclosed by the Poincare plot to evaluate heart rate variability (HRV).
Автор: Feckan, Michal Название: Poincare-Andronov-Melnikov Analysis for Non-Smooth Systems ISBN: 012804294X ISBN-13(EAN): 9780128042946 Издательство: Elsevier Science Рейтинг: Цена: 11620.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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.
Extends Melnikov analysis of the classic Poincar 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 Poincar -Andronov-Melnikov analysis can be used to solve them
Investigates the relationship between non-smooth systems and their continuous approximations
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