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Poincar Andronov Melnikov Analysis for Non Smooth Systems

Poincar   Andronov Melnikov Analysis for Non Smooth Systems
  • Author : Michal Fečkan
  • Publsiher : Academic Press
  • Release : 07 June 2016
  • ISBN : 0128043644
  • Pages : 260 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKPoincar Andronov Melnikov Analysis for Non Smooth Systems

Summary:
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


Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems
  • Author : Michal Fečkan,Michal Pospíšil
  • Publisher : Academic Press
  • Release : 07 June 2016
GET THIS BOOKPoincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

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


Modeling, Analysis And Control Of Dynamical Systems With Friction And Impacts

Modeling, Analysis And Control Of Dynamical Systems With Friction And Impacts
  • Author : Olejnik Pawel,Feckan Michal,Awrejcewicz Jan
  • Publisher : #N/A
  • Release : 07 July 2017
GET THIS BOOKModeling, Analysis And Control Of Dynamical Systems With Friction And Impacts

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


Mathematical Modelling in Health, Social and Applied Sciences

Mathematical Modelling in Health, Social and Applied Sciences
  • Author : Hemen Dutta
  • Publisher : Springer Nature
  • Release : 29 February 2020
GET THIS BOOKMathematical Modelling in Health, Social and Applied Sciences

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



Elements of Applied Bifurcation Theory

Elements of Applied Bifurcation Theory
  • Author : Yuri Kuznetsov
  • Publisher : Springer Science & Business Media
  • Release : 09 March 2013
GET THIS BOOKElements of Applied Bifurcation Theory

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,


Piecewise-smooth Dynamical Systems

Piecewise-smooth Dynamical Systems
  • Author : Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk
  • Publisher : Springer Science & Business Media
  • Release : 01 January 2008
GET THIS BOOKPiecewise-smooth Dynamical Systems

This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.


Ordinary Differential Equations and Dynamical Systems

Ordinary Differential Equations and Dynamical Systems
  • Author : Gerald Teschl
  • Publisher : American Mathematical Soc.
  • Release : 30 August 2012
GET THIS BOOKOrdinary Differential Equations and Dynamical Systems

This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the


Distribution of Sequences

Distribution of Sequences
  • Author : Oto Strauch,Štefan Porubský
  • Publisher : Peter Lang Publishing
  • Release : 03 March 2021
GET THIS BOOKDistribution of Sequences

The monograph covers material scattered throughout books and journals and focuses on the distribution properties of sequences which may be expressed in terms of distribution function, upper and lower distribution function, the discrepancy, diaphony, dispersion etc. The individual character of sequences reflected in their distribution properties may be an object of study from various points of view, and as such they are often the primary goal of investigation. In that case the studied properties are caught in separate results and



Introduction to Applied Nonlinear Dynamical Systems and Chaos

Introduction to Applied Nonlinear Dynamical Systems and Chaos
  • Author : Stephen Wiggins
  • Publisher : Springer Science & Business Media
  • Release : 18 April 2006
GET THIS BOOKIntroduction to Applied Nonlinear Dynamical Systems and Chaos

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik


Non-Smooth Dynamical Systems

Non-Smooth Dynamical Systems
  • Author : Markus Kunze
  • Publisher : Springer
  • Release : 06 May 2007
GET THIS BOOKNon-Smooth Dynamical Systems

The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.


Nonsmooth Mechanics

Nonsmooth Mechanics
  • Author : Bernard Brogliato
  • Publisher : Springer
  • Release : 29 February 2016
GET THIS BOOKNonsmooth Mechanics

Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to issues connected with control and modelling. It covers Lagrangian and Newton–Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given detailed exposition connected


Ordinary Differential Equations with Applications

Ordinary Differential Equations with Applications
  • Author : Carmen Chicone
  • Publisher : Springer Science & Business Media
  • Release : 08 April 2008
GET THIS BOOKOrdinary Differential Equations with Applications

Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory


Handbook of Global Analysis

Handbook of Global Analysis
  • Author : Demeter Krupka,David Saunders
  • Publisher : Elsevier
  • Release : 11 August 2011
GET THIS BOOKHandbook of Global Analysis

This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics. This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable


Nonlinear Ordinary Differential Equations

Nonlinear Ordinary Differential Equations
  • Author : Dominic Jordan,P. Smith,Peter Smith
  • Publisher : Oxford University Press on Demand
  • Release : 23 August 2007
GET THIS BOOKNonlinear Ordinary Differential Equations

Thoroughly updated and expanded 4th edition of the classic text, including numerous worked examples, diagrams and exercises. An ideal resource for students and lecturers in engineering, mathematics and the sciences it is published alongside a separate Problems and Solutions Sourcebook containing over 500 problems and fully-worked solutions.