• Home
  • Poincar Andronov Melnikov Analysis for Non Smooth Systems

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

Book Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems PDF Download/ Read Online



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

Book Modeling, Analysis And Control Of Dynamical Systems With Friction And Impacts PDF Download/ Read Online


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

Book Mathematical Modelling in Health, Social and Applied Sciences PDF Download/ Read Online


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,

Book Elements of Applied Bifurcation Theory PDF Download/ Read Online


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

Book Ordinary Differential Equations and Dynamical Systems PDF Download/ Read Online


Nonlinear Dynamics and Chaos

Nonlinear Dynamics and Chaos
  • Author : Steven H. Strogatz
  • Publisher : CRC Press
  • Release : 04 May 2018
GET THIS BOOKNonlinear Dynamics and Chaos

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Book Nonlinear Dynamics and Chaos PDF Download/ Read Online


Bifurcation and Chaos in Nonsmooth Mechanical Systems

Bifurcation and Chaos in Nonsmooth Mechanical Systems
  • Author : Jan Awrejcewicz,Claude-Henri Lamarque
  • Publisher : World Scientific
  • Release : 28 January 2022
GET THIS BOOKBifurcation and Chaos in Nonsmooth Mechanical Systems

This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical

Book Bifurcation and Chaos in Nonsmooth Mechanical Systems PDF Download/ Read Online


Introduction to Mechanics and Symmetry

Introduction to Mechanics and Symmetry
  • Author : Jerrold E. Marsden,Tudor S. Ratiu
  • Publisher : Springer Science & Business Media
  • Release : 19 March 2013
GET THIS BOOKIntroduction to Mechanics and Symmetry

A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a

Book Introduction to Mechanics and Symmetry PDF Download/ Read Online


Ordinary Differential Equations with Applications

Ordinary Differential Equations with Applications
  • Author : Carmen Chicone
  • Publisher : Springer Science & Business Media
  • Release : 23 September 2006
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

Book Ordinary Differential Equations with Applications PDF Download/ Read Online


Qualitative Theory of Planar Differential Systems

Qualitative Theory of Planar Differential Systems
  • Author : Freddy Dumortier,Jaume Llibre,Joan C. Artés
  • Publisher : Springer Science & Business Media
  • Release : 13 October 2006
GET THIS BOOKQualitative Theory of Planar Differential Systems

This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal

Book Qualitative Theory of Planar Differential Systems PDF Download/ Read Online


Normal Modes and Localization in Nonlinear Systems

Normal Modes and Localization in Nonlinear Systems
  • Author : Alexander F. Vakakis
  • Publisher : Springer Science & Business Media
  • Release : 29 June 2013
GET THIS BOOKNormal Modes and Localization in Nonlinear Systems

The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear

Book Normal Modes and Localization in Nonlinear Systems PDF Download/ Read Online


Differential Dynamical Systems, Revised Edition

Differential Dynamical Systems, Revised Edition
  • Author : James D. Meiss
  • Publisher : SIAM
  • Release : 24 January 2017
GET THIS BOOKDifferential Dynamical Systems, Revised Edition

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the

Book Differential Dynamical Systems, Revised Edition PDF Download/ Read Online


Differential Equations, Dynamical Systems, and an Introduction to Chaos

Differential Equations, Dynamical Systems, and an Introduction to Chaos
  • Author : Morris W. Hirsch,Stephen Smale,Robert L. Devaney
  • Publisher : Academic Press
  • Release : 28 January 2022
GET THIS BOOKDifferential Equations, Dynamical Systems, and an Introduction to Chaos

This text is about the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It is an update of one of Academic Press's most successful mathematics texts ever published, which has become the standard textbook for graduate courses in this area. The authors are tops in the field of advanced mathematics. Steve Smale is a Field's Medalist, which equates to being a Nobel prize winner in mathematics. Bob Devaney has authored

Book Differential Equations, Dynamical Systems, and an Introduction to Chaos PDF Download/ Read Online


Nonlinear Ordinary Differential Equations

Nonlinear Ordinary Differential Equations
  • Author : Dominic Jordan,Peter Smith
  • Publisher : OUP Oxford
  • Release : 24 August 2007
GET THIS BOOKNonlinear Ordinary Differential Equations

This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents. Over 500 end-of-chapter problems are also included and as an additional

Book Nonlinear Ordinary Differential Equations PDF Download/ Read Online