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Poincare Andronov Melnikov Analysis For Non Smooth Systems

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Poincar Andronov Melnikov Analysis for Non Smooth Systems

Poincar   Andronov Melnikov Analysis for Non Smooth Systems Book
Author : Michal Fečkan,Michal Pospíšil
Publisher : Academic Press
Release : 2016-06-07
ISBN : 0128043644
Language : En, Es, Fr & De

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Book Description :

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

Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts

Modeling  Analysis And Control Of Dynamical Systems With Friction And Impacts Book
Author : Olejnik Pawel,Feckan Michal,Awrejcewicz Jan
Publisher : #N/A
Release : 2017-07-07
ISBN : 9813225300
Language : En, Es, Fr & De

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Book Description :

This book is aimed primarily towards physicists and mechanical engineers specializing in modeling, analysis, and control of discontinuous systems with friction and impacts. It fills a gap in the existing literature by offering an original contribution to the field of discontinuous mechanical systems based on mathematical and numerical modeling as well as the control of such systems. Each chapter provides the reader with both the theoretical background and results of verified and useful computations, including solutions of the problems of modeling and application of friction laws in numerical computations, results from finding and analyzing impact solutions, the analysis and control of dynamical systems with discontinuities, etc. The contents offer a smooth correspondence between science and engineering and will allow the reader to discover new ideas. Also emphasized is the unity of diverse branches of physics and mathematics towards understanding complex piecewise-smooth dynamical systems. Mathematical models presented will be important in numerical experiments, experimental measurements, and optimization problems found in applied mechanics.

Mathematical Modelling in Health Social and Applied Sciences

Mathematical Modelling in Health  Social and Applied Sciences Book
Author : Hemen Dutta
Publisher : Springer Nature
Release : 2020-02-29
ISBN : 9811522863
Language : En, Es, Fr & De

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Book Description :

This book discusses significant research findings in the field of mathematical modelling, with particular emphasis on important applied-sciences, health, and social issues. It includes topics such as model on viral immunology, stochastic models for the dynamics of influenza, model describing the transmission of dengue, model for human papillomavirus (HPV) infection, prostate cancer model, realization of economic growth by goal programming, modelling of grazing periodic solutions in discontinuous systems, modelling of predation system, fractional epidemiological model for computer viruses, and nonlinear ecological models. A unique addition in the proposed areas of research and education, this book is a valuable resource for graduate students, researchers and educators associated with the study of mathematical modelling of health, social and applied-sciences issues. Readers interested in applied mathematics should also find this book valuable.

Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 1998
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Mathematical Reviews book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Russian Mathematical Surveys

Russian Mathematical Surveys Book
Author : Anonim
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Russian Mathematical Surveys book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Elements of Applied Bifurcation Theory

Elements of Applied Bifurcation Theory Book
Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
Release : 1998-09-18
ISBN : 0387983821
Language : En, Es, Fr & De

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Book Description :

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Progress in Nonlinear Science

Progress in Nonlinear Science Book
Author : Lev M. Lerman
Publisher : Unknown
Release : 2002
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Progress in Nonlinear Science book written by Lev M. Lerman, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.