Piecewise-smooth Dynamical Systems, Mario Bernardo; Chris Budd; Alan Richard Champneys
Автор: Simpson David John Warwick Название: Bifurcations In Piecewise-Smooth Continuous Systems ISBN: 9814293849 ISBN-13(EAN): 9789814293846 Издательство: World Scientific Publishing Рейтинг: Цена: 15998.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. This title presents the results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. It reveals various codimension-two, discontinuity induced bifurcations.
Mark H.A. Davis introduced the Piecewise-Deterministic Markov Process (PDMP) class of stochastic hybrid models in an article in 1984. Today it is used to model a variety of complex systems in the fields of engineering, economics, management sciences, biology, Internet traffic, networks and many more. Yet, despite this, there is very little in the way of literature devoted to the development of numerical methods for PDMDs to solve problems of practical importance, or the computational control of PDMPs.
This book therefore presents a collection of mathematical tools that have been recently developed to tackle such problems. It begins by doing so through examples in several application domains such as reliability. The second part is devoted to the study and simulation of expectations of functionals of PDMPs. Finally, the third part introduces the development of numerical techniques for optimal control problems such as stopping and impulse control problems.
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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