The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Caratheodory prime ends topology and Gromov hyperbolicity theory. This work is intended both as a reference source for researchers interested in the subject, and as an introductory book for beginners with a (undergraduate) background in real and complex analysis. For this purpose, the book is self-contained and all non-standard (and, mostly, all standard) results are proved in details.

This book constitutes the proceedings of the 6th International Symposium on Chaos, Complexity and Leadership (ICCLS). Written by interdisciplinary researchers and students from the fields of mathematics, physics, education, economics, political science, statistics, the management sciences and social sciences, the peer-reviewed contributions explore chaotic and complex systems, as well as chaos and complexity theory in the context of their applicability to management and leadership. The book discusses current topics, such as complexity leadership in the healthcare fields and tourism industry, conflict management and organization intelligence, and presents practical applications of theoretical concepts, making it a valuable resource for managers and leaders.

This thesis focuses on experimental studies on collective motion using swimming bacteria as model active-matter systems. It offers comprehensive reviews of state-of-the-art theories and experiments on collective motion from the viewpoint of nonequilibrium statistical physics. The author presents his experimental studies on two major classes of collective motion that had been well studied theoretically. Firstly, swimming filamentous bacteria in a thin fluid layer are shown to exhibit true, long-range orientational order and anomalously strong giant density fluctuations, which are considered universal and landmark signatures of collective motion by many numerical and theoretical works but have never been observed in real systems. Secondly, chaotic bacterial turbulence in a three-dimensional dense suspension without any long-range order as described in the first half is demonstrated to be capable of achieving antiferromagnetic vortex order by imposing a small number of constraints with appropriate periodicity. The experimental results presented significantly advance our fundamental understanding of order and fluctuations in collective motion of motile elements and their future applications.

This book emphasizes those topological methods (of dynamical systems) and theories that are useful in the study of different classes of nonautonomous evolutionary equations. The content is developed over six chapters, providing a thorough introduction to the techniques used in the Chapters III-VI described by Chapter I-II. The author gives a systematic treatment of the basic mathematical theory and constructive methods for Nonautonomous Dynamics. They show how these diverse topics are connected to other important parts of mathematics, including Topology, Functional Analysis and Qualitative Theory of Differential/Difference Equations. Throughout the book a nice balance is maintained between rigorous mathematics and applications (ordinary differential/difference equations, functional differential equations and partial difference equations). The primary readership includes graduate and PhD students and researchers in in the field of dynamical systems and their applications (control theory, economic dynamics, mathematical theory of climate, population dynamics, oscillation theory etc).

This book presents the proceedings of the "5th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems (CCS)." All Symposia in the series bring together scientists, engineers, economists and social scientists, creating a vivid forum for discussions on the latest insights and findings obtained in the areas of complexity, nonlinear dynamics and chaos theory, as well as their interdisciplinary applications. The scope of the latest Symposium was enriched with a variety of contemporary, interdisciplinary topics, including but not limited to: fundamental theory of nonlinear dynamics, networks, circuits, systems, biology, evolution and ecology, fractals and pattern formation, nonlinear time series analysis, neural networks, sociophysics and econophysics, complexity management and global systems.

This volume presents the proceedings of the meeting New Trends in One-Dimensional Dynamics, which celebrated the 70th birthday of Welington de Melo and was held at the IMPA, Rio de Janeiro, in November 2016. Highlighting the latest results in one-dimensional dynamics and its applications, the contributions gathered here also celebrate the highly successful meeting, which brought together experts in the field, including many of Welington de Melo's co-authors and former doctoral students. Sadly, Welington de Melo passed away shortly after the conference, so that the present volume became more a tribute to him. His role in the development of mathematics was undoubtedly an important one, especially in the area of low-level dynamics, and his legacy includes, in addition to many articles with fundamental contributions, books that are required reading for all newcomers to the field.

This book presents an original combination of three well-known methodological approaches for nonlinear data analysis: recurrence, networks, and fuzzy logic. After basic concepts of these three approaches are introduced, this book presents recently developed methods known as fuzzy recurrence plots and fuzzy recurrence networks. Computer programs written in MATLAB, which implement the basic algorithms, are included to facilitate the understanding of the developed ideas. Several applications of these techniques to biomedical problems, ranging from cancer and neurodegenerative disease to depression, are illustrated to show the potential of fuzzy recurrence methods. This book opens a new door to theorists in complex systems science as well as specialists in medicine, biology, engineering, physics, computer science, geosciences, and social economics to address issues in experimental nonlinear signal and data processing.

Though there have been significant advances in the theory and applications of linear time-invariant systems, developments regarding repetitive control have been sporadic. At the same time, there is a dearth of literature on repetitive control (RC) for nonlinear systems.Addressing that gap, this book discusses a range of basic methods for solving RC problems in nonlinear systems, including two commonly used methods and three original ones. Providing valuable tools for researchers working on the development of repetitive control, these new and fundamental methods are one of the major features of the book, which will benefit researchers, engineers, and graduate students in e.g. the field of control theory.

With the exponential growth of program trading in the global financial industry, quantum finance and its underlying technologies have become one of the hottest topics in the fintech community. Numerous financial institutions and fund houses around the world require computer professionals with a basic understanding of quantum finance to develop intelligent financial systems. This book presents a selection of the author's past 15 years' R&D work and practical implementation of the Quantum Finance Forecast System - which integrates quantum field theory and related AI technologies to design and develop intelligent global financial forecast and quantum trading systems. The book consists of two parts: Part I discusses the basic concepts and theories of quantum finance and related AI technologies, including quantum field theory, quantum price fields, quantum price level modelling and quantum entanglement to predict major financial events. Part II then examines the current, ongoing R&D projects on the application of quantum finance technologies in intelligent real-time financial prediction and quantum trading systems. This book is both a textbook for undergraduate & masters level quantum finance, AI and fintech courses and a valuable resource for researchers and data scientists working in the field of quantum finance and intelligent financial systems. It is also of interest to professional traders/ quants & independent investors who would like to grasp the basic concepts and theory of quantum finance, and more importantly how to adopt this fascinating technology to implement intelligent financial forecast and quantum trading systems. For system implementation, the interactive quantum finance programming labs listed on the Quantum Finance Forecast Centre official site (QFFC.org) enable readers to learn how to use quantum finance technologies presented in the book.

This book discusses human perception and performance within the framework of the theory of self-organizing systems. To that end, it presents a variety of phenomena and experimental findings in the research field, and provides an introduction to the theory of self-organization, with a focus on amplitude equations, order parameter and Lotka-Volterra equations. The book demonstrates that relating the experimental findings to the mathematical models provides an explicit account for the causal nature of human perception and performance. In particular, the notion of determinism versus free will is discussed in this context. The book is divided into four main parts, the first of which discusses the relationship between the concept of determinism and the fundamental laws of physics. The second part provides an introduction to using the self-organization approach from physics to understand human perception and performance, a strategy used throughout the remainder of the book to connect experimental findings and mathematical models. In turn, the third part of the book focuses on investigating performance guided by perception: climbing stairs and grasping tools are presented in detail. Perceptually relevant bifurcation parameters in the mathematical models are also identified, e.g. in the context of walk-to-run gait transitions. Chains of perceptions and actions together with their underlying mechanisms are then presented, and a number of experimental phenomena - such as selective attention, priming, child play, bistable perception, retrieval-induced forgetting, functional fixedness and memory effects exhibiting hysteresis with positive or negative sign - are discussed. Human judgment making, internal experiences such as dreaming and thinking, and Freud's concept of consciousness are also addressed. The fourth and last part of the book explores several specific topics such as learning, social interactions between two people, life trajectories, and applications in clinical psychology. In particular, episodes of mania and depression under bipolar disorder, perception under schizophrenia, and obsessive-compulsive rituals are discussed. This book is intended for researchers and graduate students in psychology, physics, applied mathematics, kinesiology, and the sport sciences who want to learn about the foundations of the field. Written for a mixed audience, the experiments and concepts are presented using non-technical language throughout. In addition, each chapter includes more advanced sections for modelers in the fields of physics and applied mathematics.

This brief presents a suite of computationally efficient methods for bounding trajectories of dynamical systems with multi-dimensional intervals, or 'boxes'. It explains the importance of bounding trajectories for evaluating the robustness of systems in the face of parametric uncertainty, and for verification or control synthesis problems with respect to safety and reachability properties. The methods presented make use of: interval analysis; monotonicity theory; contraction theory; and data-driven techniques that sample trajectories. The methods are implemented in an accompanying open-source Toolbox for Interval Reachability Analysis. This brief provides a tutorial description of each method, focusing on the requirements and trade-offs relevant to the user, requiring only basic background on dynamical systems. The second part of the brief describes applications of interval reachability analysis. This makes the brief of interest to a wide range of academic researchers, graduate students, and practising engineers in the field of control and verification.

This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings.

This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.

This book is about morphogenesis as the genesis of forms. It is not restricted to plants growing from seed or animals developing from an embryo (although these do supply the most abundant examples) but also addresses kindred processes, from inorganic to social to biomorphic technology. It is about our morphogenetic universe: unplanned, unfair and frustratingly complicated but benevolent in allowing us to emerge, survive, and inquire into its laws.

The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.

This book discusses the realization and control problems of finite-dimensional dynamical systems which contain linear and nonlinear systems. The author focuses on algebraic methods for the discussion of control problems of linear and non-linear dynamical systems. The book contains detailed examples to showcase the effectiveness of the presented method. The target audience comprises primarily research experts in the field of control theory, but the book may also be beneficial for graduate students alike.

Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.

This book introduces a trans-scale framework necessary for the physical understanding of breakdown behaviors and presents some new paradigm to clarify the mechanisms underlying the trans-scale processes. The book, which is based on the interaction of mechanics and statistical physics, will help to deepen the understanding of how microdamage induces disaster and benefit the forecasting of the occurrence of catastrophic rupture. It offers notes and problems in each part as interesting background and illustrative exercises. Readers of the book would be graduate students, researchers, engineers working on civil, mechanical and geo-engineering, etc. However, people with various background but interested in disaster reduction and forecasting, like applied physics, geophysics, seismology, etc., may also be interested in the book.

This book discusses the design of new space missions and their use for a better understanding of the dynamical behaviour of solar system bodies, which is an active field of astrodynamics. Space missions gather data and observations that enable new breakthroughs in our understanding of the origin, evolution and future of our solar system and Earth's place within it. Covering topics such as satellite and space mission dynamics, celestial mechanics, spacecraft navigation, space exploration applications, artificial satellites, space debris, minor bodies, and tidal evolution, the book presents a collection of contributions given by internationally respected scientists at the summer school "Satellite Dynamics and Space Missions: Theory and Applications of Celestial Mechanics", held in 2017 at San Martino al Cimino, Viterbo (Italy). This school aimed to teach the latest theories, tools and methods developed for satellite dynamics and space, and as such the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.

This book presents a unique fusion of two different research topics. One is related to the traditional mathematical problem of chases and escapes. The problem mainly deals with a situation where a chaser pursues an evader to analyze their trajectories and capture time. It dates back more than 300 years and has developed in various directions such as differential games. The other topic is the recently developing field of collective behavior, which investigates origins and properties of emergent behavior in groups of self-driving units. Applications include schools of fish, flocks of birds, and traffic jams. This book first reviews representative topics, both old and new, from these two areas. Then it presents the combined research topic of "group chase and escape", recently proposed by the authors. Although the combination is simple and straightforward, the book describes the emergence of rather intricate behavior, provoking the interest of readers for further developments and applications of related topics.

This book presents up-to-date research developments and novel methodologies to solve various stability and control problems of dynamic systems with time delays. First, it provides the new introduction of integral and summation inequalities for stability analysis of nominal time-delay systems in continuous and discrete time domain, and presents corresponding stability conditions for the nominal system and an applicable nonlinear system. Next, it investigates several control problems for dynamic systems with delays including H(infinity) control problem Event-triggered control problems; Dynamic output feedback control problems; Reliable sampled-data control problems. Finally, some application topics covering filtering, state estimation, and synchronization are considered. The book will be a valuable resource and guide for graduate students, scientists, and engineers in the system sciences and control communities.

This volume collects the edited and reviewed contributions presented in the 8th iTi Conference on Turbulence, held in Bertinoro, Italy, in September 2018. In keeping with the spirit of the conference, the book was produced afterwards, so that the authors had the opportunity to incorporate comments and discussions raised during the event. The respective contributions, which address both fundamental and applied aspects of turbulence, have been structured according to the following main topics: I TheoryII Wall-bounded flowsIII Simulations and modellingIV ExperimentsV Miscellaneous topicsVI Wind energy

This is the proceedings of the IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems that was held in Novi Sad, Serbia, from July 15th to 19th, 2018. The appearance of nonlinear phenomena used to be perceived as dangerous, with a general tendency to avoid them or control them. This perception has led to intensive research using various approaches and tailor-made tools developed over decades. However, the Nonlinear Dynamics of today is experiencing a profound shift of paradigm since recent investigations rely on a different strategy which brings good effects of nonlinear phenomena to the forefront. This strategy has a positive impact on different fields in science and engineering, such as vibration isolation, energy harvesting, micro/nano-electro-mechanical systems, etc. Therefore, the ENOLIDES Symposium was devoted to demonstrate the benefits and to unlock the potential of exploiting nonlinear dynamical behaviour in these but also in other emerging fields of science and engineering. This proceedings is useful for researchers in the fields of nonlinear dynamics of mechanical systems and structures, and in Mechanical and Civil Engineering.

This book offers a timely overview of theories and methods developed by an authoritative group of researchers to understand the link between criticality and brain functioning. Cortical information processing in particular and brain function in general rely heavily on the collective dynamics of neurons and networks distributed over many brain areas. A key concept for characterizing and understanding brain dynamics is the idea that networks operate near a critical state, which offers several potential benefits for computation and information processing. However, there is still a large gap between research on criticality and understanding brain function. For example, cortical networks are not homogeneous but highly structured, they are not in a state of spontaneous activation but strongly driven by changing external stimuli, and they process information with respect to behavioral goals. So far the questions relating to how critical dynamics may support computation in this complex setting, and whether they can outperform other information processing schemes remain open. Based on the workshop "Dynamical Network States, Criticality and Cortical Function", held in March 2017 at the Hanse Institute for Advanced Studies (HWK) in Delmenhorst, Germany, the book provides readers with extensive information on these topics, as well as tools and ideas to answer the above-mentioned questions. It is meant for physicists, computational and systems neuroscientists, and biologists.

This book focuses on the latest applications of nonlinear approaches in engineering and addresses a range of scientific problems. Examples focus on issues in automotive technology, including automotive dynamics, control for electric and hybrid vehicles, and autodriver algorithm for autonomous vehicles. Also included are discussions on renewable energy plants, data modeling, driver-aid methods, and low-frequency vibration. Chapters are based on invited contributions from world-class experts who advance the future of engineering by discussing the development of more optimal, accurate, efficient, cost, and energy effective systems. This book is appropriate for researchers, students, and practising engineers who are interested in the applications of nonlinear approaches to solving engineering and science problems. Presents a broad range of practical topics and approaches; Explains approaches to better, safer, and cheaper systems; Emphasises automotive applications, physical meaning, and methodologies.