Download or read book Topology And Dynamics Of Chaos In Celebration Of Robert Gilmore s 70th Birthday written by Christophe Letellier and published by World Scientific. This book was released on 2013-01-11 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included.The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto Rössler, René Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively.Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical — not necessarily widely known — contributions (about the different types of chaos introduced by Rössler and not just the “Rössler attractor”; Gumowski and Mira's contributions in electronics; Poincaré's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc.

Download or read book Encyclopedia of Knot Theory written by Colin Adams and published by CRC Press. This book was released on 2021-02-10 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory

Download or read book Chaos In Nature Second Edition written by Christophe Letellier and published by World Scientific. This book was released on 2019-04-26 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the history of chaos theory, from celestial mechanics (three-body problem) to electronics and meteorology. Many illustrative examples of chaotic behaviors exist in various contexts found in nature (chemistry, astrophysics, biomedicine). This book includes the most popular systems from chaos theory (Lorenz, Rössler, van der Pol, Duffing, logistic map, Lozi map, Hénon map etc.) and introduces many other systems, some of them very rarely discussed in textbooks as well as in scientific papers. The contents are formulated with an original approach as compared to other books on chaos theory.

Download or read book Coupled Phase locked Loops Stability Synchronization Chaos And Communication With Chaos written by Valery V Matrosov and published by World Scientific. This book was released on 2018-08-29 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern technological, biological, and socioeconomic systems are extremely complex. The study of such systems largely relies on the concepts of competition and cooperation (synchronization). The main approaches to the study of nonlinear dynamics of complex systems are now associated with models of collective dynamics of networks and ensembles, formed by interacting dynamical elements.Unfortunately, the applicability of analytical and qualitative methods of nonlinear dynamics to such complex systems is severely restricted due to the high dimension of phase space. Therefore, studying the simplest models of networks, which are ensembles with a small number of elements, becomes of particular interest. Such models allow to make use of the entire spectrum of analytical, qualitative, and numerical methods of nonlinear dynamics. This book is devoted to the investigation of a kind of such systems, namely small ensembles of coupled, phase-controlled oscillators. Both traditional issues, like synchronization, that are relevant for applications in radio-communications, radio-location, energy, etc., and nontraditional issues of excitation of chaotic oscillations and their possible application in advanced communication systems are addressed.

Download or read book Deterministic Chaos In One Dimensional Continuous Systems written by Jan Awrejcewicz and published by World Scientific. This book was released on 2016-03-14 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations.Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler-Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic-plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels.The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.

Download or read book Toward General Theory Of Differential operator And Kinetic Models written by Nikolay Sidorov and published by World Scientific. This book was released on 2020-03-13 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive introduction to the modern theory of differential-operator and kinetic models including Vlasov-Maxwell, Fredholm, Lyapunov-Schmidt branching equations to name a few. This book will bridge the gap in the considerable body of existing academic literature on the analytical methods used in studies of complex behavior of differential-operator equations and kinetic models. This monograph will be of interest to mathematicians, physicists and engineers interested in the theory of such non-standard systems.

Download or read book Control Of Imperfect Nonlinear Electromechanical Large Scale Systems From Dynamics To Hardware Implementation written by Luigi Fortuna and published by World Scientific. This book was released on 2017-05-19 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a class of uncertain systems that are called imperfect, and shows how much systems can regularly work if an appropriate control strategy is adopted. Along with some practical well studied examples, a formalization of the models for imperfect system is considered and a control strategy is proposed. Experimental case studies on electromechanical systems are also included.New concepts, experimental innovative circuits and laboratory details allow the reader to implement at low cost the outlined strategy. Emergent topics in nonlinear device realization are emphasized with the aim to allow researchers and students to perform experiments with large scale electromechanical systems. Moreover, the possibility of using imperfections and noise to generate nonlinear strange behavior is discussed.

Download or read book Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts written by Pawel Olejnik and published by #N/A. This book was released on 2017-07-07 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Modeling Love Dynamics written by Sergio E. T. Al RINALDI and published by World Scientific. This book was released on 2015-10-22 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows, for the very first time, how love stories -- a vital issue in our lives -- can be tentatively described with classical mathematics. Focus is on the derivation and analysis of reliable models that allow one to formally describe the expected evolution of love affairs from the initial state of indifference to the final romantic regime. The models are in full agreement with the basic philosophical principles of love psychology. Eight chapters are theoretically oriented and discuss the romantic relationships between important classes of individuals identified by particular psychological traits. The remaining chapters are devoted to case studies described in classical poems or in worldwide famous films.

Download or read book Continuous And Discontinuous Piecewise smooth One dimensional Maps Invariant Sets And Bifurcation Structures written by Viktor Avrutin and published by World Scientific. This book was released on 2019-05-28 with total page 649 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 Frequency domain Approach To Hopf Bifurcation Analysis Continuous Time delayed Systems written by Franco Sebastian Gentile and published by World Scientific. This book was released on 2019-10-07 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of an effective frequency-domain approach, based on systems control theory, to compute and analyze several types of standard bifurcation conditions for general continuous-time nonlinear dynamical systems. A very rich pictorial gallery of local bifurcation diagrams for such nonlinear systems under simultaneous variations of several system parameters is presented. Some higher-order harmonic balance approximation formulas are derived for analyzing the oscillatory dynamics in small neighborhoods of certain types of Hopf and degenerate Hopf bifurcations.The frequency-domain approach is then extended to the large class of delay-differential equations, where the time delays can be either discrete or distributed. For the case of discrete delays, two alternatives are presented, depending on the structure of the underlying dynamical system, where the more general setting is then extended to the case of distributed time-delayed systems. Some representative examples in engineering and biology are discussed.

Download or read book Integral Dynamical Models Singularities Signals And Control written by Denis Sidorov and published by World Scientific. This book was released on 2014-09-05 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering, operations research and image analysis.

Download or read book Wave Momentum And Quasi particles In Physical Acoustics written by Gerard A Maugin and published by World Scientific. This book was released on 2015-03-26 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume presents an original approach to physical acoustics with additional emphasis on the most useful surface acoustic waves on solids. The study is based on foundational work of Léon Brillouin, and application of the celebrated invariance theorem of Emmy Noether to an element of volume that is representative of the wave motion.This approach provides an easy interpretation of typical wave motions of physical acoustics in bulk, at surfaces, and across interfaces, in the form of the motion of associated quasi-particles. This type of motion, Newtonian or not, depends on the wave motion considered, and on the original modeling of the continuum that supports it. After a thoughtful review of Brillouin's fundamental ideas related to radiative stresses, wave momentum and action, and the necessary reminder on modern nonlinear continuum thermomechanics, invariance theory and techniques of asymptotics, a variety of situations and models illustrates the power and richness of the approach and its strong potential in applications. Elasticity, piezoelectricity and new models of continua with nonlinearity, viscosity and some generalized features (microstructure, weak or strong nonlocality) or unusual situations (bounding surface with energy, elastic thin film glued on a surface waveguide), are considered, exhibiting thus the versatility of the approach.This original book offers an innovative vision and treatment of the problems of wave propagation in deformable solids. It opens up new horizons in the theoretical and applied facets of physical acoustics.

Download or read book A Nonlinear Dynamics Perspective of Wolfram s New Kind of Science written by Leon O. Chua and published by World Scientific. This book was released on 2013 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text uncovers secret recipes from the abstract theory of one-dimensional cellular automata for predicting the long-term evolution of a ring of identical elementary cells where the binary state of each cell during each generation of an attractor is determined uniquely by the state of its left and right neighbors in the previous generation, as decreed by one of 256 truth tables.

Download or read book Nonlinear Dynamics Perspective Of Wolfram s New Kind Of Science A Volume Vi written by Leon O Chua and published by World Scientific. This book was released on 2013-07-10 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable volume ends the quest to uncover the secret recipes for predicting the long-term evolution of a ring of identical elementary cells where the binary state of each cell during each generation of an attractor (i.e. after the transients had disappeared) is determined uniquely by the state of its left and right neighbors in the previous generation, as decreed by one of 256 truth tables. As befitting the contents aimed at school children, it was found pedagogically appealing to code each truth table by coloring each of the 8 vertices of a cubical graph in red (for binary state 1), or blue (for binary state 0), forming a toy universe of 256 Boolean cubes, each bearing a different vertex color combination.The corresponding collection of 256 distinct Boolean cubes are then segegrated logically into 6 distinct groups where members from each group share certain common dynamics which allow the long-term evolution of the color configuration of each bit string, of arbitrary length, to be predicted painlessly, via a toy-like gaming procedure, without involving any calculation. In particular, the evolution of any bit string bearing any initial color configuration which resides in any one of the possibly many distinct attractors, can be systematically predicted, by school children who are yet to learn arithmetic, via a simple recipe, for any Boolean cube belonging to group 1, 2, 3, or 4. The simple recipe for predicting the time-asymptotic behaviors of Boolean cubes belonging to groups 1, 2, and 3 has been covered in Vols. I, II, ..., V.This final volume continues the recipe for each of the 108, out of 256, local rules, dubbed the Bernoulli rules, belonging to group 4. Here, for almost half of the toy universe, surprisingly simple recipes involving only the following three pieces of information are derived in Vol. VI; namely, a positive integer τ, a positive, or negative, integer σ, and a sign parameter β > 0, or β 0. In particular, given any color configuration belonging to an attractor of any one of the 108 Boolean cubes from group 4, any child can predict the color configuration after τ generations, without any computation, by merely shifting each cell σ bits to the left (resp. right) if σ 0 (resp. σ

Download or read book Advances in Wave Turbulence written by Victor Shrira and published by World Scientific. This book was released on 2013 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave or weak turbulence is a branch of science concerned with the evolution of random wave fields of all kinds and on all scales, from waves in galaxies to capillary waves on water surface, from waves in nonlinear optics to quantum fluids. In spite of the enormous diversity of wave fields in nature, there is a common conceptual and mathematical core which allows us to describe the processes of random wave interactions within the same conceptual paradigm, and in the same language. The development of this core and its links with the applications is the essence of wave turbulence science (WT) which is an established integral part of nonlinear science.

Download or read book Discontinuity Nonlinearity and Complexity written by Lev Ostrovsky and published by L& H Scientific Publishing. This book was released on 2018-07-01 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interdisciplinary journal publishes original and new results on recent developments, discoveries and progresses on Discontinuity, Nonlinearity and Complexity in physical and social sciences. The aim of the journal is to stimulate more research interest for exploration of discontinuity, complexity, nonlinearity and chaos in complex systems. The manuscripts in dynamical systems with nonlinearity and chaos are solicited, which includes mathematical theories and methods, physical principles and laws, and computational techniques. The journal provides a place to researchers for the rapid exchange of ideas and techniques in discontinuity, complexity, nonlinearity and chaos in physical and social sciences. No length limitations for contributions are set, but only concisely written manuscripts are published. Brief papers are published on the basis of Technical Notes. Discussions of previous published papers are welcome. Topics of Interest Complex and hybrid dynamical systemsDiscontinuous dynamical systems (i.e., impulsive, time-delay, flow barriers)Nonlinear discrete systems and symbolic dynamicsFractional dynamical systems and controlStochastic dynamical systems and randomnessComplexity, self-similarity and synchronization in nonlinear physicsNonlinear phenomena and physical mechanismsStability, bifurcation and chaos in complex systemsHydrodynamics, turbulence and complexity mechanismNonlinear waves and solitonDynamical networksCombinatorial aspects of dynamical systemsBiological dynamics and biophysics