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Complex Time-Delay Systems
One of the major contemporary challenges in both physical and social sciences is modeling, analyzing, and understanding the self-organization, evolution, behavior, and eventual decay of complex dynamical systems ranging from cell assemblies to the human brain to animal societies. The multi-faceted problems in this domain require a wide range of methods from various scienti?c disciplines. There is no question that the inclusion of time delays in complex system models considerably enriches the challenges presented by the problems. Although this inclusion often becomes inevitable as real-world applications demand more and more realistic m- els, the role of time delays in the context of complex ...
Topics in Time Delay Systems
Time delays are present in many physical processes due to the period of time it takes for the events to occur. Delays are particularly more pronounced in networks of interconnected systems, such as supply chains and systems controlled over c- munication networks. In these control problems, taking the delays into account is particularly important for performance evaluation and control system’s design. It has been shown, indeed, that delays in a controlled system (for instance, a c- munication delay for data acquisition) may have an “ambiguous” nature: they may stabilize the system, or, in the contrary,they may lead to deteriorationof the clos- loop performance or even instability, depen...
Networks: From Biology to Theory
Recent decades have witnessed the thriving development of new mathematical, computational and theoretical approaches, such as bioinformatics and neuroinformatics, to tackle fundamental issues in biology. These approaches focus no longer on individual units, such as nerve cells or genes, but rather on dynamic patterns of interactions between them. This volume explores the concept in full, featuring contributions from a global group of contributors, many of whom are pre-eminent in their field.
Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 3
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 third volume concentrates on reviewing further relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such fluctuation relations and chaotic dynamics in physics, fractals and their applications in epileptic seizures, as well as chaos synchronization. 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.
Discrete and Continuous Models in the Theory of Networks
This book contains contributions from the participants of the research group hosted by the ZiF - Center for Interdisciplinary Research at the University of Bielefeld during the period 2013-2017 as well as from the conclusive conference organized at Bielefeld in December 2017. The contributions consist of original research papers: they mirror the scientific developments fostered by this research program or the state-of-the-art results presented during the conclusive conference. The volume covers current research in the areas of operator theory and dynamical systems on networks and their applications, indicating possible future directions. The book will be interesting to researchers focusing on the mathematical theory of networks; it is unique as, for the first time, continuous network models - a subject that has been blooming in the last twenty years - are studied alongside more classical and discrete ones. Thus, instead of two different worlds often growing independently without much intercommunication, a new path is set, breaking with the tradition. The fruitful and beneficial exchange of ideas and results of both communities is reflected in this book.
Mathematical Modeling of Biological Systems, Volume II
Volume II of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout are mathematical and computational apporaches to examine central problems in the life sciences, ranging from the organization principles of individual cells to the dynamics of large populations. The chapters are thematically organized into the following main areas: epidemiology, evolution and ecology, immunology, neural systems and the brain, and innovative mathematical methods and education. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Algebraic and Symbolic Computation Methods in Dynamical Systems
This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has be...
Time Delay Systems: Methods, Applications and New Trends
This volume is concerned with the control and dynamics of time delay systems; a research field with at least six-decade long history that has been very active especially in the past two decades. In parallel to the new challenges emerging from engineering, physics, mathematics, and economics, the volume covers several new directions including topology induced stability, large-scale interconnected systems, roles of networks in stability, and new trends in predictor-based control and consensus dynamics. The associated applications/problems are described by highly complex models, and require solving inverse problems as well as the development of new theories, mathematical tools, numerically-tractable algorithms for real-time control. The volume, which is targeted to present these developments in this rapidly evolving field, captures a careful selection of the most recent papers contributed by experts and collected under five parts: (i) Methodology: From Retarded to Neutral Continuous Delay Models, (ii) Systems, Signals and Applications, (iii): Numerical Methods, (iv) Predictor-based Control and Compensation, and (v) Networked Control Systems and Multi-agent Systems.
Control of Self-Organizing Nonlinear Systems
The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.
