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This book aims to propose the implementation and application of Fractional Order Systems (FOS). It is well known that FOS can be utilized in control applications and systems modeling, and their effectiveness has been proven in many theoretical works and simulation routines. A further and mandatory step for FOS real world utilization is their hardware implementation and applications on real systems modeling. With this viewpoint, introductory chapters are included on the definition of stability region of Fractional Order PID Controller and Chaotic FOS, followed by the practical implementation based on Microcontroller, Field Programmable Gate Array, Field Programmable Analog Array and Switched Capacitor. Another section is dedicated to FO modeling of Ionic Polymeric Metal Composite (IPMC). This new material will have applications in robotics, aerospace and biomedicine.

Nonlinear time series methods have developed rapidly over a quarter of a century and have reached an advanced state of maturity during the last decade. Implementations of these methods for experimental data are now widely accepted and fairly routine; however, genuinely useful applications remain rare. This book focuses on the practice of applying these methods to solve real problems. To illustrate the usefulness of these methods, a wide variety of physical and physiological systems are considered. The technical tools utilized in this book fall into three distinct, but interconnected areas: quantitative measures of nonlinear dynamics, Monte-Carlo statistical hypothesis testing, and nonlinear modeling. Ten highly detailed applications serve as case studies of fruitful applications and illustrate the mathematical techniques described in the text.

Systems theorists see common principles in the structure and operation of systems of all kinds and sizes. They promote an interdisciplinary science adapted for a universal application with a common language and area of concepts. In order to solve problems, make recommendations and predict the future, they use theories, models and concepts from the vast area of general systems theory.

Differential-algebraic equations (DAEs) provide an essential tool for system modeling and analysis within different fields of applied sciences and engineering. This book addresses modeling issues and analytical properties of DAEs, together with some applications in electrical circuit theory.

For engineering applications that are based on nonlinear phenomena, novel information processing systems require new methodologies and design principles. This perspective is the basis of the three cornerstones of this book: cellular neural networks, chaos and synchronization. Cellular neural networks and their universal machine implementations offer a well-established platform for processing spatial-temporal patterns and wave computing. Multi-scroll circuits are generalizations to the original Chua's circuit, leading to chip implementable circuits with increasingly complex attractors. Several applications make use of synchronization techniques for nonlinear systems. A systematic overview is given for Lur'e representable systems with global synchronization criteria for master-slave and mutual synchronization, robust synchronization, H∞ synchronization, time-delayed systems and impulsive synchronization.

A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory.

This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models. The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asymptotic split and merging schemes. Most of the results from semi-Markov processes are new and presented for the first time in this book.

This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field — including some innovations by the authors themselves — that have not appeared in any other book.

In the history of physics and science, quantum mechanics has served as the foundation of modern science. This book discusses the properties of microscopic particles in nonlinear systems, principles of the nonlinear quantum mechanical theory, and its applications in condensed matter, polymers and biological systems. The book is essentially composed of three parts. The first part presents a review of linear quantum mechanics, as well as theoretical and experimental fundamentals that establish the nonlinear quantum mechanical theory. The theory itself and its essential features are covered in the second part. In the final part, extensive applications of this theory in physics, biology and polymer are introduced. The whole volume forms a complete system of nonlinear quantum mechanics.

Piecewise constant systems exist in widely expanded areas such as engineering, physics, and mathematics. Extraordinary and complex characteristics of piecewise constant systems have been reported in recent years. This book provides the methodologies for analyzing and assessing nonlinear piecewise constant systems on a theoretically and practically sound basis.