Das Buch wendet sich an Leser, die - uber die rein computergraphische Darstellung hinaus - an einer analytischen Untersuchung von chaotischen und nichtchaotischen Differenzen- und Differentialgleichungssystemen interessiert sind. Breiter Raum wird der Durchrechnung von Beispielen gegeben. Dargestellt werden zunachst qualitative Methoden als auch solche, die das Auffinden von Attraktoren, Bifurkationen etc. und deren Klassifikation in Abhangigkeit von den Systemparametern gestatten. Der letzte Teil schliesslich widmet sich der quantitativen Beschreibung chaotischer Systeme. Dazu werden zuerst die Begriffe Chaos und Fraktal exakt definiert und dann die verschiedenen fraktalen Dimensionen, Lyapunov-Exponenten, Entropien etc. eingefuhrt und durch Beispiele begrundet."

Twentieth-century research in the field of chemical pattern formation saw extraordinary progress due to the pathbreaking contributions of Nobel laureate Ilya Prigogine and his co-workers. Evidence exists that the dissipative structures studied by Prigogine and his colleagues may play a dominant role in the processes of self-organization of biological systems, the fundamental phenomena that govern all life forms. Brought together in this valuable volume are topical papers from the this research. Important aspects of nonlinear chemical pattern formation-dissipative structures-in chemical, biochemical, and geological systems are surveyed by leading scientists in the field of nonlinear chemistry. Topics covered include experimental observations of pattern formation in a variety of systems, bifurcation theory and analysis of nonlinear chemical rate equations, and the stochastic theory of nonlinear chemical reactions. Of particular interest are the studies of the effects of electric fields on the determination of nonequilibrium states of chemical systems.

The contributions to this volume attempt to apply different aspects of Ilya Prigogine's Nobel-prize-winning work on dissipative structures to nonchemical systems as a way of linking the natural and social sciences. They address both the mathematical methods for description of pattern and form as they evolve in biological systems and the mechanisms of the evolution of social systems, containing many variables responding to subjective, qualitative stimuli. The mathematical modeling of human systems, especially those far from thermodynamic equilibrium, must involve both chance and determinism, aspects both quantitative and qualitative. Such systems (and the physical states of matter which they resemble) are referred to as self-organized or dissipative structures in order to emphasize their dependence on the flows of matter and energy to and from their surroundings. Some such systems evolve along lines of inevitable change, but there occur instances of choice, or bifurcation, when chance is an important factor in the qualitative modification of structure. Such systems suggest that evolution is not a system moving toward equilibrium but instead is one which most aptly evokes the patterns of the living world. The volume is truly interdisciplinary and should appeal to researchers in both the physical and social sciences. Based on a workshop on dissipative structures held in 1978 at the University of Texas, contributors include Prigogine, A. G. Wilson, Andre de Palma, D. Kahn, J. L. Deneubourgh, J. W. Stucki, Richard N. Adams, and Erick Jantsch. The papers presented include Allen, "Self-Organization in the Urban System"; Robert Herman, "Remarks on Traffic Flow Theories and the Characterization of Traffic in Cities"; W. H. Zurek and Schieve, "Nucleation Paradigm: Survival Threshold in Population Dynamics"; De Palma et al., "Boolean Equations with Temporal Delays"; Nicholas Georgescu-Roegin, "Energy Analysis and Technology Assessment"; Magoroh Maruyama, "Four Different Causal Meta-types in Biological and Social Sciences"; and Jantsch, "From Self-Reference to Self-Transcendence: The Evolution of Self-Organization Dynamics."

This thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds. The local dynamics of holomorphic maps around critical points is still not completely understood, in dimension 2 or higher, due to the richness of the geometry of the critical set for all iterates. In dimension 2, the study of the dynamics induced on a suitable functional space (the valuative tree) allows a classification of such maps up to birational conjugacy, reducing the problem to the special class of rigid germs, where the geometry of the critical set is simple. In some cases, from such dynamical data one can construct special compact complex surfaces, called Kato surfaces, related to some conjectures in complex geometry.

This book provides research summaries from a number of different focuses in Mathematics, and compiles biographical sketches of top professionals in this important field.

H Robust design is an advancing technology which aims to achieve the system design purpose under intrinsic random fluctuation and external disturbance. This book introduces several robust design methods, some of which include linear to nonlinear systems and frequency to time domain. This book provides not only a complete theoretical development and application of H robust design over the last three decades, but also an integrated platform for control, signal processing, communication, systems and synthetic biology. Based on the theoretical H robust design results, the authors also give some practical design examples to illustrate the procedure and validate the performance of the proposed H method with computational simulations and tables.

This book reviews topics on the areas of fixed point theory, convex and set-valued analysis, variational inequality and complementarity problem theory, non-linear ergodic theory, difference, differential and integral equations, control and optimisation theory, dynamic system theory, inequality theory, stochastic analysis and probability theory, and their applications.

This book focuses on recent advances made in the field of non-linear dynamic modelling in economics. Mathematically, linearity is a very special kind of relation between variables chosen to the purpose of simplification. Even in physics linear modelling of dynamical systems was a first choice for quite some time, due to convenience in analysis, as exemplified by the acceleration law, the harmonic oscillator, the wave equation, and the like. The methods of analysis were simply developed to the ease of dealing with such systems. These methods are found under the heading of infinitesimal calculus; at early stages dynamical processes were formulated as differential equations in continuous time.

This book reviews recent topics on the areas of fixed point theory, convex and set-valued analysis, variational inequality and complementarity problem theory, non-linear ergodic theory, difference, differential and integral equations, control and optimisation theory, dynamic system theory, inequality theory, stochastic analysis and probability theory, and their applications.

Covering one of the fastest growing areas of applied mathematics, Nonlinear Dynamics and Chaos: Second Edition, is a fully updated edition of this highly respected text. Covering a breadth of topics, ranging from the basic concepts to applications in the physical sciences, the book is highly illustrated and written in a clear and comprehensible style.

• Provides a self-contained introduction to the theory and applications of nonlinear dynamics and chaos.

• Introduces the concepts of instabilities, bifurcations, and catastrophes.

• Each idea is carefully explained and supported by examples.

• Features many applications to a wide variety of scientific fields.

• Includes an illustrated glossary of geometrical dynamics.

• Features a supplementary bibliography of further reading.

• Assumes minimal background knowledge.

This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods converging in the study of foliations. The lectures by Aziz El Kacimi Alaoui provide an introduction to Foliation Theory with emphasis on examples and transverse structures. Steven Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations: limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, Pesin Theory and hyperbolic, parabolic and elliptic types of foliations. The lectures by Masayuki Asaoka compute the leafwise cohomology of foliations given by actions of Lie groups, and apply it to describe deformation of those actions. In his lectures, Ken Richardson studies the properties of transverse Dirac operators for Riemannian foliations and compact Lie group actions, and explains a recently proved index formula. Besides students and researchers of Foliation Theory, this book will be interesting for mathematicians interested in the applications to foliations of subjects like Topology of Manifolds, Differential Geometry, Dynamics, Cohomology or Global Analysis.

The book is designed to serve as a textbook for courses offered to upper-undergraduate students enrolled in physics. The first edition of this book was published in 2014. As there is a demand for the next edition, it is quite natural to take note of the several advances that have occurred in the subject over the past five years and to decide which of these are appropriate for inclusion at the textbook level, given the fundamental nature and the significance of the subject area. This is the prime motivation for bringing out a revised second edition. Among the newer mechanisms and materials, the book introduces the super-continuum generation, which arises from an excellent interplay of the various mechanisms of optical nonlinearity. The topics covered in this book are quantum mechanics of nonlinear interaction of matter and radiation, formalism and phenomenology of nonlinear wave mixing processes, optical phase conjugation and applications, self-focusing and self-phase modulation and their role in pulse modification, nonlinear absorption mechanisms, and optical limiting applications, photonic switching and bi-stability, and physical mechanisms leading to a nonlinear response in a variety of materials. This book has emerged from an attempt to address the requirement of presenting the subject at the college level. This textbook includes rigorous features such as the elucidation of relevant basic principles of physics; a clear exposition of the ideas involved at an appropriate level; coverage of the physical mechanisms of non-linearity; updates on physical mechanisms and emerging photonic materials and emphasis on the experimental study of nonlinear interactions. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in physics and related courses.

Sliding mode control was first introduced in the 1950s. It is a nonlinear control technique with many unique properties. In this book, different aspects of SMC are explored. Chapters include new developments in research on a sliding mode governor for hydropower plants; integral sliding mode control (I-SMC) for a variable speed wind turbine system and a I-SMC method for load frequency control (LFC) of nonlinear power systems with wind turbines; the control of a stand-alone photovoltaic (PV) system; leader-follower-based formation control of a group of mobile robots; the application of Takagi-Sugeno (T-S) fuzzy model in coordinated control of multiple robots system; an induction motor speed control using the nonsingular terminal sliding-mode control method; adaptive nonsingular terminal sliding mode (NTSM) tracking control scheme based on backstepping design presented for Micro-Electro-Mechanical Systems (MEMS) vibratory gryoscopes; and a hybrid actuator and its control using a cascade sliding mode technique.

Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer. The text includes some items not previously published.

This book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose-Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross-Pitaevskii equations. Based on the Heisenberg model of spin-spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.

Statistical Thermodynamics: An Engineering Approach covers in a practical, readily understandable manner the underlying meaning of entropy, temperature and other thermodynamic concepts, the foundations of quantum mechanics, and the physical basis of gas, liquid and solid phase properties. It presents simply the relationship between macroscopic and microscopic thermodynamics. In addition, the molecular basis of transport phenomena and chemical kinetics are explored, as are basic concepts in spectroscopy. Modern computational tools for solving thermodynamic problems are explored, and the student is assured that he or she will gain knowledge of practical usefulness. This essential text is suitable for mechanical or aerospace engineering graduate students who have a strong background in engineering thermodynamics, those entering advanced fields such as combustion, high temperature gas dynamics, environmental sciences, or materials processing, and those who wish to build a background for understanding advanced experimental diagnostic techniques in these or similar fields.

This second edition of the book, Nonlinear Random Vibration: Analytical Techniques and Applications, expands on the original edition with additional detailed steps in various places in the text. It is a first systematic presentation on the subject. Its features include: * a concise treatment of Markovian and non- Markovian solutions of nonlinear stochastic differential equations, * exact solutions of Fokker-Planck-Kolmogorov equations, * methods of statistical linearization, * statistical nonlinearization techniques, * methods of stochastic averaging, * truncated hierarchy techniques, and * an appendix on probability theory. A special feature is its incorporation of detailed steps in many examples of engineering applications. Targeted audience: Graduates, research scientists and engineers in mechanical, aerospace, civil and environmental (earthquake, wind and transportation), automobile, naval, architectural, and mining engineering.

This volume is the proceedings of the 14th MSJ International Research Institute "Asymptotic Analysis and Singularity", which was held at Sendai, Japan in July 2005. The proceedings contain survey papers and original research papers on nonlinear partial differential equations, dynamical systems, calculus of variations and mathematical physics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

Nonlinear dynamo theory is central to our understanding of the magnetic structures of planets, stars and galaxies. This volume presents an updated and coherent view of recent advances in this significant and expanding area with contributions from some of the leading authors in the field. Both kinetic and dynamic approaches to the subject are considered with topics including fast dynamos, topological methods in dynamo theory, physics of the solar cycle and the fundamentals of mean field dynamo. This volume provides a useful source of reference for graduate students and researchers in theoretical astrophysics and applied mathematics interested in cosmic magnetism and related topics such as turbulence, convection and more general nonlinear physics.