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Chaos, Nonlinearity, Complexity by Ashok Sengupta Pdf
This book explores non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems, drawing on relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It offers a self-contained theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.
Nonlinearity, Chaos, and Complexity by Cristoforo Sergio Bertuglia,Franco Vaio Pdf
Covering a broad range of topics and adopting a detailed philosophical approach to the subject, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences.
Complex Nonlinearity by Vladimir G. Ivancevic,Tijana T. Ivancevic Pdf
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.
Chaos, Complexity and Leadership 2020 by Şefika Şule Erçetin,Şuay Nilhan Açıkalın,Emir Vajzović Pdf
This book analyzes a range of new developments in various fields concerning the concepts of chaos and complexity theory. The proceedings of the 7th International Symposium on Chaos, Complexity and Leadership feature newly developed concepts involving various research methodologies for identifying chaos and complexity in different fields of the sciences and leadership. In addition, it explores chaotic and complex systems from all fields of knowledge in order to stake a claim of prevalence of compatibility between knowledge fields. Particular emphasis is placed on exploring non-linearity in order to open a discussion on new approaches to and perspectives on chaos, complexity and leadership. Readers will find coverage of important events that have recently taken place in our world, regardless of whether they were social, political, economic or scientific in nature. The book explores diverse aspects of and issues related to the effects of chaos and complexity in the world; discusses the application of nonlinear dynamics in order to arrive at transformational policies; and offers projections of tomorrow’s world using an interdisciplinary approach. Though primarily intended for readers with an interest in nonlinear science, thanks to its focus on the application of chaos and complexity to other disciplines, the book appeals to a broad readership.
Chaos, Nonlinearity, Complexity by Ashok Sengupta Pdf
This book explores non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems, drawing on relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It offers a self-contained theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.
Nonlinear Dynamics and Chaos: Advances and Perspectives by Marco Thiel,Jürgen Kurths,M. Carmen Romano,György Károlyi,Alessandro Moura Pdf
This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.
This book differs from others on Chaos Theory in that it focuses on its applications for understanding complex phenomena. The emphasis is on the interpretation of the equations rather than on the details of the mathematical derivations. The presentation is interdisciplinary in its approach to real-life problems: it integrates nonlinear dynamics, nonequilibrium thermodynamics, information theory, and fractal geometry. An effort has been made to present the material ina reader-friendly manner, and examples are chosen from real life situations. Recent findings on the diagnostics and control of chaos are presented, and suggestions are made for setting up a simple laboratory. Included is a list of topics for further discussion that may serve not only for personal practice or homework, but also as themes for theses, dissertations, and research proposals. Includes laboratory experiments Includes applications and case studies related to cell differentiation, EKGs, and immunology Presents interdisciplinary applications of chaos theory to complex systems Emphasizes the meaning of mathematical equations rather than their derivations Features reader friendly presentation with many illustrations and interpretations Deals with real life, dissipative systemsIntegrates mathematical theory throughout the text
Chaos and Complexity Theory for Management: Nonlinear Dynamics by Banerjee, Santo Pdf
Although chaos theory refers to the existence between seemingly random events, it has been gaining the attention of science, technology and managements fields. The shift from traditional procedures to the dynamics of chaos and complexity theory has resulted in a new element of complexity thinking, allowing for a greater capability for analyzing and understanding key business processes. Chaos and Complexity Theory for Management: Nonlinear Dynamics explores chaos and complexity theory and its relationship with the understanding of natural chaos in the business environment. Utilizing these theories aids in comprehending the development of businesses as a complex adaptive system.
Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf
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.
Nonlinear Dynamics and Chaos by J Hogan,A.R Krauskopf,Mario di Bernado,R. Eddie Wilson,Hinke. M Osinga,Martin. E Homer,Alan. R Champneys Pdf
Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such systems? Written by international experts, Nonlinear Dynamics and Chaos: Where Do We Go from Here? assesses what the future holds for dynamics and chaos. The chapters address one or more of the broad and interconnected main themes: neural and biological systems, spatially extended systems, and experimentation in the physical sciences. The contributors offer suggestions as to what they see as the way forward, often in the form of open questions for future research.
Nonlinear Psychoanalysis by Robert M. Galatzer-Levy Pdf
Nonlinear concepts from chaos theory, complexity studies, and fractal geometry have transformed the way we think about the mind. Nonlinear Psychoanalysis shows how nonlinear dynamics can be integrated with psychoanalytic thinking to shed new light on psychological development, therapeutic processes, and fundamental psychoanalytic concepts. Starting with a personal history of the author’s engagement with nonlinear dynamics and psychoanalysis, this book describes how his approach applies to diagnosis of psychological conditions, concepts of normal and pathological development, gender, research methods, and finally the theory and practice of psychoanalysis and psychodynamic psychotherapy. This book is full of new ideas about the basic nonlinear processes of human development, nonlinear views of gender and fundamental psychoanalytic process like working through, and the nature of the therapeutic process as conceptualized in terms of the theory of coupled oscillators. Galatzer-Levy questions many standard psychoanalytic formulations and points to a freer practice of psychoanalysis and psychoanalytic thinking. His new approach opens the reader’s eyes to ways in which development and treatment can occur through processes not now included in standard psychoanalytic theory. The book not only provides useful theories but also helps readers take note of commonly passed over phenomena that were unseen for lack of a theory to explain them. Galatzer-Levy brings an unusual combination of training in psychiatry, psychoanalysis, and mathematics to this unique study, which summarizes his forty years of exploration of nonlinearity and psychoanalysis. Nonlinear Psychoanalysis will appeal to psychoanalysts and psychotherapists as well as students of nonlinear dynamics systems.
Measures of Complexity and Chaos by Neal B. Abraham,Alfonso M. Albano,Anthony Passamante,Paul E. Rapp Pdf
This volume serves as a general introduction to the state of the art of quantitatively characterizing chaotic and turbulent behavior. It is the outgrowth of an international workshop on "Quantitative Measures of Dynamical Complexity and Chaos" held at Bryn Mawr College, June 22-24, 1989. The workshop was co-sponsored by the Naval Air Development Center in Warminster, PA and by the NATO Scientific Affairs Programme through its special program on Chaos and Complexity. Meetings on this subject have occurred regularly since the NATO workshop held in June 1983 at Haverford College only two kilometers distant from the site of this latest in the series. At that first meeting, organized by J. Gollub and H. Swinney, quantitative tests for nonlinear dynamics and chaotic behavior were debated and promoted [1). In the six years since, the methods for dimension, entropy and Lyapunov exponent calculations have been applied in many disciplines and the procedures have been refined. Since then it has been necessary to demonstrate quantitatively that a signal is chaotic rather than it being acceptable to observe that "it looks chaotic". Other related meetings have included the Pecos River Ranch meeting in September 1985 of G. Mayer Kress [2) and the reflective and forward looking gathering near Jerusalem organized by M. Shapiro and I. Procaccia in December 1986 [3). This meeting was proof that interest in measuring chaotic and turbulent signals is widespread.
Recent Trends In Chaotic, Nonlinear And Complex Dynamics by Jan Awrejcewicz,Rajasekar Shanmuganathan,Minvydas Ragulskis Pdf
In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.
William A. Brock,David Arthur Hsieh,Blake Dean LeBaron
Author : William A. Brock,David Arthur Hsieh,Blake Dean LeBaron Publisher : MIT Press Page : 362 pages File Size : 44,7 Mb Release : 1991 Category : Business & Economics ISBN : 0262023296
Nonlinear Dynamics, Chaos, and Instability by William A. Brock,David Arthur Hsieh,Blake Dean LeBaron Pdf
Brock, Hsieh, and LeBaron show how the principles of chaos theory can be applied to such areas of economics and finance as the changing structure of stock returns and nonlinearity in foreign exchange.
Handbook of Nonlinearity, Chaos, and Complexity Methods for Scientists and Engineers by Vladimir G. Ivancevic,Tijana T. Ivancevic Pdf
This book contains an easytofollow essence of non-linearity, chaos and complexity methods for modelling complex dynamical systems, extracted from our seven graduate-level monographs. Topics discussed include the basics of non-linear and chaotic dynamics; chaos in continuous and discrete dynamics; non-linear complexity in neurodynamics and cancer dynamics; non-linear complexity in injury dynamics; non-linear complexity in crowd dynamics and spatio-temporal complexity.