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Nonlinearity, Chaos, and Complexity by Cristoforo Sergio Bertuglia,Franco Vaio Pdf
Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique text in the midst of many current books on chaos and complexity. Part 1 deals with the mathematical model as an instrument of investigation. The general meaning of modelling and, more specifically, questions concerning linear modelling are discussed. Part 2 deals with the theme of chaos and the origin of chaotic dynamics. Part 3 deals with the theme of complexity: a property of the systems and of their models which is intermediate between stability and chaos. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.
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.
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.
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.
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.
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.
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.
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, 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.
Applications of Chaos and Nonlinear Dynamics in Engineering - by Santo Banerjee,Mala Mitra,Lamberto Rondoni Pdf
Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications
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.
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.
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.
At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.
