Download or read book Bifurcations in Piecewise Smooth Continuous Systems written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bifurcations in Piecewise smooth Continuous Systems written by David John Warwick Simpson and published by World Scientific. This book was released on 2010 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. NeimarkSacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.

Download or read book Bifurcations and Chaos in Piecewise smooth Dynamical Systems written by Zhanybai T. Zhusubaliyev and published by World Scientific. This book was released on 2003 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.

Download or read book Piecewise smooth Dynamical Systems written by Mario Bernardo and published by Springer Science & Business Media. This book was released on 2008-01-01 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Continuous And Discontinuous Piecewise smooth One dimensional Maps Invariant Sets And Bifurcation Structures written by Gardini Laura and published by World Scientific. This book was released on 2019-05-28 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.

Download or read book Elements of Applied Bifurcation Theory written by Yuri Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Extended Abstracts Spring 2016 written by Alessandro Colombo and published by Birkhäuser. This book was released on 2017-05-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the "Intensive Research Program on Advances in Nonsmooth Dynamics 2016", held at the Centre de Recerca Matemàtica (CRM) in Barcelona from February 1st to April 29th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and outlines of prominent discussion sessions. The articles are all the result of direct collaborations initiated during the research program. The topic is the theory and applications of Nonsmooth Dynamics. This includes systems involving elements of: impacting, switching, on/off control, hybrid discrete-continuous dynamics, jumps in physical properties, and many others. Applications include: electronics, climate modeling, life sciences, mechanics, ecology, and more. Numerous new results are reported concerning the dimensionality and robustness of nonsmooth models, shadowing variables, numbers of limit cycles, discontinuity-induced bifurcations and chaos, determinacy-breaking, stability criteria, and the classification of attractors and other singularities. This material offers a variety of new exciting problems to mathematicians, but also a diverse range of new tools and insights for scientists and engineers making use of mathematical modeling and analysis. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

Download or read book Bifurcations in Continuous Piecewise Linear Differential Systems written by Enrique Ponce and published by Springer Nature. This book was released on 2022-12-10 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the qualitative study of differential equations defined by piecewise linear (PWL) vector fields, mainly continuous, and presenting two or three regions of linearity. The study focuses on the more common bifurcations that PWL differential systems can undergo, with emphasis on those leading to limit cycles. Similarities and differences with respect to their smooth counterparts are considered and highlighted. Regarding the dimensionality of the addressed problems, some general results in arbitrary dimensions are included. The manuscript mainly addresses specific aspects in PWL differential systems of dimensions 2 and 3, which are sufficinet for the analysis of basic electronic oscillators. The work is divided into three parts. The first part motivates the study of PWL differential systems as the natural next step towards dynamic complexity when starting from linear differential systems. The nomenclature and some general results for PWL systems in arbitrary dimensions are introduced. In particular, a minimal representation of PWL systems, called canonical form, is presented, as well as the closing equations, which are fundamental tools for the subsequent study of periodic orbits. The second part contains some results on PWL systems in dimension 2, both continuous and discontinuous, and both with two or three regions of linearity. In particular, the focus-center-limit cycle bifurcation and the Hopf-like bifurcation are completely described. The results obtained are then applied to the study of different electronic devices. In the third part, several results on PWL differential systems in dimension 3 are presented. In particular, the focus-center-limit cycle bifurcation is studied in systems with two and three linear regions, in the latter case with symmetry. Finally, the piecewise linear version of the Hopf-pitchfork bifurcation is introduced. The analysis also includes the study of degenerate situations. Again, the above results are applied to the study of different electronic oscillators.

Download or read book Dynamics and Bifurcations of Non Smooth Mechanical Systems written by Remco I. Leine and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Download or read book Bifurcation and Chaos in Discontinuous and Continuous Systems written by Michal Fečkan and published by Springer Science & Business Media. This book was released on 2011-05-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving difference equations, ordinary and partial differential equations, differential equations with impulses, piecewise smooth differential equations, differential and difference inclusions, and differential equations on infinite lattices as well. This book is intended for mathematicians, physicists, theoretically inclined engineers and postgraduate students either studying oscillations of nonlinear mechanical systems or investigating vibrations of strings and beams, and electrical circuits by applying the modern theory of bifurcation methods in dynamical systems. Dr. Michal Fečkan is a Professor at the Department of Mathematical Analysis and Numerical Mathematics on the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovakia. He is working on nonlinear functional analysis, bifurcation theory and dynamical systems with applications to mechanics and vibrations.

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Download or read book Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields written by John Guckenheimer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Download or read book Introduction to Nonlinear Aeroelasticity written by Grigorios Dimitriadis and published by John Wiley & Sons. This book was released on 2017-03-10 with total page 863 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Nonlinear Aeroelasticity Introduces the latest developments and technologies in the area of nonlinear aeroelasticity Nonlinear aeroelasticity has become an increasingly popular research area in recent years. There have been many driving forces behind this development, increasingly flexible structures, nonlinear control laws, materials with nonlinear characteristics and so on. Introduction to Nonlinear Aeroelasticity covers the theoretical basics in nonlinear aeroelasticity and applies the theory to practical problems. As nonlinear aeroelasticity is a combined topic, necessitating expertise from different areas, the book introduces methodologies from a variety of disciplines such as nonlinear dynamics, bifurcation analysis, unsteady aerodynamics, non-smooth systems and others. The emphasis throughout is on the practical application of the theories and methods, so as to enable the reader to apply their newly acquired knowledge Key features: Covers the major topics in nonlinear aeroelasticity, from the galloping of cables to supersonic panel flutter Discusses nonlinear dynamics, bifurcation analysis, numerical continuation, unsteady aerodynamics and non-smooth systems Considers the practical application of the theories and methods Covers nonlinear dynamics, bifurcation analysis and numerical methods Accompanied by a website hosting Matlab code Introduction to Nonlinear Aeroelasticity is a comprehensive reference for researchers and workers in industry and is also a useful introduction to the subject for graduate and undergraduate students across engineering disciplines.

Download or read book Differential Dynamical Systems Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.

Download or read book Nonlinearity written by and published by . This book was released on 2009-04 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bifurcations in discontinuous mechanical systems of Filippov type written by Remco Ingmar Leine and published by . This book was released on 2000 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Robust Chaos and Its Applications written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2012 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.