This study applies the findings of the new nonlinear sciences to understanding the processes of growing complexity and intensifying chaos in the modern world. It also identifies and reviews approaches for living and coping with these trends. Uri Merry seeks to clarify the role of chaos in the transformation of the social sciences to new orders by re-examining and re-evaluating some of the basic tenets of modern social and behavioral science in light of theories of chaos, self-organization, and complexity. Divided into three sections, the work provides an overview of the major findings of the new science of chaos; analyzes why chaos is on the upsurge and why human society is experiencing such anxiety about it; and surveys some of the major approaches for dealing with chaos in society, organizations, and our personal lives.

This book aims to present a survey of a large class of nonlinear dynamical systems exhibiting mixed-mode oscillations (MMOs). It is a sort of a guide to systems related to MMOs that features material from original research papers, including the author's own studies. The material is presented in seven chapters divided into sections. Usually, the first sections are of an introductory nature, explain phenomena, and exhibit numerical results. More advanced investigations are presented in the subsequent sections. Coverage includes * Dynamic behavior of nonlinear systems, * Fundamentals of processes exhibiting MMOs,* Mechanism and function of an structure of MMOs patterns, * Analysis of MMOs in electric circuits and systems, * MMOs in chemistry, biology, and medicine, * MMOs in mechanics and transport vehicles, * MMOs in fractional order systems. This is the first extensive description of these topics and the interpretation of analytical results and those obtained from computer simulations with the MATLAB environment. The book provides the readers with better understanding of the nature of MMOs, richness of their behaviors, and interesting applications.

This book provides a comprehensive overview of statistical descriptions of turbulent flows. Its main objectives are to point out why ordinary perturbative treatments of the Navier-Stokes equation have been rather futile, and to present recent advances in non-perturbative treatments, e.g., the instanton method and a stochastic interpretation of turbulent energy transfer. After a brief introduction to the basic equations of turbulent fluid motion, the book outlines a probabilistic treatment of the Navier-Stokes equation and chiefly focuses on the emergence of a multi-point hierarchy and the notion of the closure problem of turbulence. Furthermore, empirically observed multiscaling features and their impact on possible closure methods are discussed, and each is put into the context of its original field of use, e.g., the renormalization group method is addressed in relation to the theory of critical phenomena. The intended readership consists of physicists and engineers who want to get acquainted with the prevalent concepts and methods in this research area.

This book highlights recent research on interval methods for solving nonlinear constraint satisfaction, optimization and similar problems. Further, it presents a comprehensive survey of applications in various branches of robotics, artificial intelligence systems, economics, control theory, dynamical systems theory, and others. Three appendices, on the notation, representation of numbers used as intervals' endpoints, and sample implementations of the interval data type in several programming languages, round out the coverage.

This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the Eighth International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2019), which took place in Lisbon, Portugal, on December 10-12, 2019. The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, and network dynamics; diffusion, epidemics, and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks; and technological networks.

This book gives a general introduction to theoretically understand thermodynamic properties and response to applied fields of mesoscopic systems that closely relate to experiments. The book clarifies many conceptual and practical problems associated with the Larmor clock and thus makes it a viable approach to study these properties. The book is written pedagogically so that a graduate or undergraduate student can follow it. This book also opens up new research areas related to the unification of classical and quantum theories and the meaning of time. It provides a scientific mechanism for time travel which is of immense fascination to science as well as society. It is known that developments in mesoscopic physics can lead to downscaling of device sizes. So, new or experienced researchers can have a quick introduction to various areas in which they might contribute in the future. This book is expected to be a valuable addition to the subject of mesoscopic physics.

There is an increasing demand for dynamic systems to become more safe and reliable. This requirement extends beyond the normally accepted safety-critical systems of nuclear reactors and aircraft where safety is paramount important, to systems such as autonomous vehicles and fast railways where the system availability is vital. It is clear that fault diagnosis (including fault detection and isolation, FDI) has been becoming an important subject in modern control theory and practice. For example, the number of papers on FDI presented in many control-related conferences has been increasing steadily. The subject of fault detection and isolation continues to mature to an established field of research in control engineering. A large amount of knowledge on model-based fault diagnosis has been ac cumulated through the literature since the beginning of the 1970s. However, publications are scattered over many papers and a few edited books. Up to the end of 1997, there is no any book which presents the subject in an unified framework. The consequence of this is the lack of "common language," dif ferent researchers use different terminology. This problem has obstructed the progress of model-based FDI techniques and has been causing great concern in research community. Many survey papers have been published to tackle this problem. However, a book which presents the materials in a unified format and provides a comprehensive foundation of model-based FDI is urgently needed."

This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants. The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the fractional integral and fractional derivative on fractal functions in various scenarios. Further, the existence of the fractal interpolation function with the countable iterated function system is demonstrated by taking suitable monotone and bounded sequences. It also covers the dimension of fractal functions and investigates the relationship between the fractal dimension and the fractional order of fractal interpolation functions. Moreover, this book explores the idea of fractal interpolation in the reconstruction scheme of illustrative waveforms and discusses the problems of identification of the characterizing parameters. In the application section, this research compendium addresses the signal processing and its Mathematical methodologies. A wavelet-based denoising method for the recovery of electroencephalogram (EEG) signals contaminated by nonstationary noises is presented, and the author investigates the recognition of healthy, epileptic EEG and cardiac ECG signals using multifractal measures. This book is intended for professionals in the field of Mathematics, Physics and Computer Science, helping them broaden their understanding of fractal functions and dimensions, while also providing the illustrative experimental applications for researchers in biomedicine and neuroscience.

This book presents collaborative research presented by experts in the field of nonlinear science provides the reader with contemporary, cutting-edge, research works that bridge the gap between theory and device realizations of nonlinear phenomena. The conference provides a unique forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: chaos gates, social networks, communication, sensors, lasers, molecular motors, biomedical anomalies, and stochastic resonance. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2018) held in Maui, Hawaii, 2018. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.

This monograph is devoted to the analysis and solution of singular differential games and singular $H_{\inf}$ control problems in both finite- and infinite-horizon settings. Expanding on the authors' previous work in this area, this novel text is the first to study the aforementioned singular problems using the regularization approach. After a brief introduction, solvability conditions are presented for the regular differential games and $H_{\inf}$ control problems. In the following chapter, the authors solve the singular finite-horizon linear-quadratic differential game using the regularization method. Next, they apply this method to the solution of an infinite-horizon type. The last two chapters are dedicated to the solution of singular finite-horizon and infinite-horizon linear-quadratic $H_{\inf}$ control problems. The authors use theoretical and real-world examples to illustrate the results and their applicability throughout the text, and have carefully organized the content to be as self-contained as possible, making it possible to study each chapter independently or in succession. Each chapter includes its own introduction, list of notations, a brief literature review on the topic, and a corresponding bibliography. For easier readability, detailed proofs are presented in separate subsections. Singular Linear-Quadratic Zero-Sum Differential Games and $H_{\inf}$ Control Problems will be of interest to researchers and engineers working in the areas of applied mathematics, dynamic games, control engineering, mechanical and aerospace engineering, electrical engineering, and biology. This book can also serve as a useful reference for graduate students in these area

This book focuses on the fault diagnosis observer design for the switched system. Model-based fault diagnosis and fault tolerant control are one of the most popular research directions in recent decades. It contains eight chapters. Every chapter is independent in the method of observer design, but all chapters are around the same topic. Besides, in each chapter, the model description and theoretical results are firstly provided, then some practical application examples are illustrated to prove the obtained results. The advanced theoretical methodologies will benefit researchers or engineers in the area of safety engineering and the arrangement of the structure will help the readers to understand the content easily.

This book offers fundamental information on the analysis and synthesis of continuous and sampled data control systems. It includes all the required preliminary materials (from mathematics, signals and systems) that are needed in order to understand control theory, so readers do not have to turn to other textbooks. Sampled data systems have recently gained increasing importance, as they provide the basis for the analysis and design of computer-controlled systems. Though the book mainly focuses on linear systems, input/output approaches and state space descriptions are also provided. Control structures such as feedback, feed forward, internal model control, state feedback control, and the Youla parameterization approach are discussed, while a closing section outlines advanced areas of control theory. Though the book also contains selected examples, a related exercise book provides Matlab/Simulink exercises for all topics discussed in the textbook, helping readers to understand the theory and apply it in order to solve control problems. Thanks to this combination, readers will gain a basic grasp of systems and control, and be able to analyze and design continuous and discrete control systems.

This monograph explores the design of controllers that suppress oscillations and instabilities in congested traffic flow using PDE backstepping methods. The first part of the text is concerned with basic backstepping control of freeway traffic using the Aw-Rascle-Zhang (ARZ) second-order PDE model. It begins by illustrating a basic control problem - suppressing traffic with stop-and-go oscillations downstream of ramp metering - before turning to the more challenging case for traffic upstream of ramp metering. The authors demonstrate how to design state observers for the purpose of stabilization using output-feedback control. Experimental traffic data are then used to calibrate the ARZ model and validate the boundary observer design. Because large uncertainties may arise in traffic models, adaptive control and reinforcement learning methods are also explored in detail. Part II then extends the conventional ARZ model utilized until this point in order to address more complex traffic conditions: multi-lane traffic, multi-class traffic, networks of freeway segments, and driver use of routing apps. The final chapters demonstrate the use of the Lighthill-Whitham-Richards (LWR) first-order PDE model to regulate congestion in traffic flows and to optimize flow through a bottleneck. In order to make the text self-contained, an introduction to the PDE backstepping method for systems of coupled first-order hyperbolic PDEs is included. Traffic Congestion Control by PDE Backstepping is ideal for control theorists working on control of systems modeled by PDEs and for traffic engineers and applied scientists working on unsteady traffic flows. It will also be a valuable resource for researchers interested in boundary control of coupled systems of first-order hyperbolic PDEs.

This book discusses methods and algorithms for the near-optimal adaptive control of nonlinear systems, including the corresponding theoretical analysis and simulative examples, and presents two innovative methods for the redundancy resolution of redundant manipulators with consideration of parameter uncertainty and periodic disturbances. It also reports on a series of systematic investigations on a near-optimal adaptive control method based on the Taylor expansion, neural networks, estimator design approaches, and the idea of sliding mode control, focusing on the tracking control problem of nonlinear systems under different scenarios. The book culminates with a presentation of two new redundancy resolution methods; one addresses adaptive kinematic control of redundant manipulators, and the other centers on the effect of periodic input disturbance on redundancy resolution. Each self-contained chapter is clearly written, making the book accessible to graduate students as well as academic and industrial researchers in the fields of adaptive and optimal control, robotics, and dynamic neural networks.

This book presents a unified mathematical treatment of diverse problems in the general domain of robotics and associated fields using Clifford or geometric alge- bra. By addressing a wide spectrum of problems in a common language, it offers both fresh insights and new solutions that are useful to scientists and engineers working in areas related with robotics. It introduces non-specialists to Clifford and geometric algebra, and provides ex- amples to help readers learn how to compute using geometric entities and geomet- ric formulations. It also includes an in-depth study of applications of Lie group theory, Lie algebra, spinors and versors and the algebra of incidence using the universal geometric algebra generated by reciprocal null cones. Featuring a detailed study of kinematics, differential kinematics and dynamics using geometric algebra, the book also develops Euler Lagrange and Hamiltoni- ans equations for dynamics using conformal geometric algebra, and the recursive Newton-Euler using screw theory in the motor algebra framework. Further, it comprehensively explores robot modeling and nonlinear controllers, and discusses several applications in computer vision, graphics, neurocomputing, quantum com- puting, robotics and control engineering using the geometric algebra framework. The book also includes over 200 exercises and tips for the development of future computer software packages for extensive calculations in geometric algebra, and a entire section focusing on how to write the subroutines in C++, Matlab and Maple to carry out efficient geometric computations in the geometric algebra framework. Lastly, it shows how program code can be optimized for real-time computations. An essential resource for applied physicists, computer scientists, AI researchers, roboticists and mechanical and electrical engineers, the book clarifies and demon- strates the importance of geometric computing for building autonomous systems to advance cognitive systems research.

This book is a novel tutorial for research-oriented study of vibration mechanics. The book begins with twelve open problems from six case studies of vibration mechanics in order to guide readers in studying the entire book. Then, the book surveys both theories and methods of linear vibrations in an elementary course from a new perspective of aesthetics of science so as to assist readers to upgrade their way of learning. The successive chapters offer a theoretical frame of linear vibrations and waves, covering the models of vibration systems, the vibration analysis of discrete systems, the natural vibrations of one-dimensional structures, the natural vibrations of symmetric structures, and the waves and vibrations of one-dimensional structures. The chapters help readers solve the twelve open problems step by step during the research-oriented study. The book tries to arouse the interest of graduate students and professionals, who have learnt an elementary course of vibration mechanics of two credits, to conduct the research-oriented study and achieve a helical upgrade understanding to vibration mechanics.

A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic SchrAdinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.

Organizations of all kinds struggle to understand, adapt, respond and manipulate changing conditions in their internal and external environments. Approaches based on the causal, linear logic of mechanistic sciences and engineering continue to play an important role, given people's ability to create order. But such approaches are valid only within carefully circumscribed boundaries. They become counterproductive when the same organizations display the highly reflexive, context-dependent, dynamic nature of systems in which agents learn and adapt and new patterns emerge. The rapidly expanding discussion about complex systems offers important contributions to the integration of diverse perspectives and ultimately new insights into organizational effectiveness. There is increasing interest in complexity in mainstream business education, as well as in specialist business disciplines such as knowledge management. Real world systems can't be completely designed, controlled, understood or predicted, even by the so-called sciences of complexity, but they can be more effective when understood as complex systems. While many scientific disciplines explore complexity principally through abstract mathematical models and simulations, Emergence: Complexity & Organization explores the emerging understanding of human systems from both the 'hard' quantitative sciences and the 'soft' qualitative perspectives. This 2010 Annual includes articles from Goktu Morcol, Lynne Hamill, Mika Aaltonen, Glenda Eoyang, Lasse Gerrits, Jean Boulton, and many more, that explore a range of complexity-related topics from philosophical concerns through to the practical application of complexity ideas, concepts and frameworks in human organizations. Also included are a series of four reproductions of classic papers in the fields of complexity and systems, each with critical introductions that explore their modern relevance: "The Science of 'Muddling' Through" by Charles E. Lindblom (originally published in 1959); "Why is Economics not an Evolutionary Science?" by Thorstein Veblen (originally published in 1898); "The Theory of Emergence" by Reuben Ablowitz (originally published in 1939), and; "Determinism and Life" by Conrad Hal Waddington (originally published in 1972).

The Abel Symposia volume at hand contains a collection of high-quality articles written by the world's leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.

This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the Eighth International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2019), which took place in Lisbon, Portugal, on December 10-12, 2019. The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, and network dynamics; diffusion, epidemics, and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks; and technological networks.

Approximation Methods in Engineering and Science covers fundamental and advanced topics in three areas: Dimensional Analysis, Continued Fractions, and Stability Analysis of the Mathieu Differential Equation. Throughout the book, a strong emphasis is given to concepts and methods used in everyday calculations. Dimensional analysis is a crucial need for every engineer and scientist to be able to do experiments on scaled models and use the results in real world applications. Knowing that most nonlinear equations have no analytic solution, the power series solution is assumed to be the first approach to derive an approximate solution. However, this book will show the advantages of continued fractions and provides a systematic method to develop better approximate solutions in continued fractions. It also shows the importance of determining stability chart of the Mathieu equation and reviews and compares several approximate methods for that. The book provides the energy-rate method to study the stability of parametric differential equations that generates much better approximate solutions.

This book presents the latest advances in computational intelligence and data analytics for sustainable future smart cities. It focuses on computational intelligence and data analytics to bring together the smart city and sustainable city endeavors. It also discusses new models, practical solutions and technological advances related to the development and the transformation of cities through machine intelligence and big data models and techniques. This book is helpful for students and researchers as well as practitioners.

Hybrid System Identification helps readers to build mathematical models of dynamical systems switching between different operating modes, from their experimental observations. It provides an overview of the interaction between system identification, machine learning and pattern recognition fields in explaining and analysing hybrid system identification. It emphasises the optimization and computational complexity issues that lie at the core of the problems considered and sets them aside from standard system identification problems. The book presents practical methods that leverage this complexity, as well as a broad view of state-of-the-art machine learning methods. The authors illustrate the key technical points using examples and figures to help the reader understand the material. The book includes an in-depth discussion and computational analysis of hybrid system identification problems, moving from the basic questions of the definition of hybrid systems and system identification to methods of hybrid system identification and the estimation of switched linear/affine and piecewise affine models. The authors also give an overview of the various applications of hybrid systems, discuss the connections to other fields, and describe more advanced material on recursive, state-space and nonlinear hybrid system identification. Hybrid System Identification includes a detailed exposition of major methods, which allows researchers and practitioners to acquaint themselves rapidly with state-of-the-art tools. The book is also a sound basis for graduate and undergraduate students studying this area of control, as the presentation and form of the book provides the background and coverage necessary for a full understanding of hybrid system identification, whether the reader is initially familiar with system identification related to hybrid systems or not.

Explains multi-level models of enterprise systems and covers modeling methodology This book addresses the essential phenomena underlying the overall behaviors of complex systems and enterprises. Understanding these phenomena can enable improving these systems. These phenomena range from physical, behavioral, and organizational, to economic and social, all of which involve significant human components. Specific phenomena of interest and how they are represented depend on the questions of interest and the relevant domains or contexts. Modeling and Visualization of Complex Systems and Enterprises examines visualization of phenomena and how understanding the relationships among phenomena can provide the basis for understanding where deeper exploration is warranted. The author also reviews mathematical and computational models, defined very broadly across disciplines, which can enable deeper understanding. Presents a 10 step methodology for addressing questions associated with the design or operation of complex systems and enterprises Examines six archetypal enterprise problems including two from healthcare, two from urban systems, and one each from financial systems and defense systems Provides an introduction to the nature of complex systems, historical perspectives on complexity and complex adaptive systems, and the evolution of systems practice Modeling and Visualization of Complex Systems and Enterprises is written for graduate students studying systems science and engineering and professionals involved in systems science and engineering, those involved in complex systems such as healthcare delivery, urban systems, sustainable energy, financial systems, and national security.

Perturbation Methods in Science and Engineering provides the fundamental and advanced topics in perturbation methods in science and engineering, from an application viewpoint. This book bridges the gap between theory and applications, in new as well as classical problems. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications in different engineering disciplines. The book begins with a clear description on limits of mathematics in providing exact solutions and goes on to show how pioneers attempted to search for approximate solutions of unsolvable problems. Through examination of special applications and highlighting many different aspects of science, this text provides an excellent insight into perturbation methods without restricting itself to a particular method. This book is ideal for graduate students in engineering, mathematics, and physical sciences, as well as researchers in dynamic systems.