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This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of nonlinearity is a universal feature in mathematics, physics, chemistry and biology, and is used to characterize systems whose behavior does not amount to a superposition of simple building blocks, but rather features complex and often chaotic patterns and phenomena. Each chapter of the book features a synopsis that not only recaps the recent progress in each field but also charts the challenges that lie ahead. This interdisciplinary book presents contributions from a diverse group of experts from various fields to provide an overview of each field’s past, present and future. It will appeal to both beginners and seasoned researchers in nonlinear science, numerous areas of physics (optics, quantum physics, biophysics), and applied mathematics (ODEs, PDEs, dynamical systems, machine learning) as well as engineering.

Nonlinear systems. --- Systems, Nonlinear --- System theory --- Statistical physics. --- Physics. --- System theory. --- Mathematical physics. --- Systems biology. --- Biological systems. --- Quantum computers. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Applications of Graph Theory and Complex Networks. --- Complex Systems. --- Theoretical, Mathematical and Computational Physics. --- Systems Biology. --- Quantum Computing. --- Computers --- Biosystems --- Systems, Biological --- Biology --- Systems biology --- Computational biology --- Bioinformatics --- Biological systems --- Molecular biology --- Physical mathematics --- Physics --- Systems, Theory of --- Systems science --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematical statistics --- Philosophy --- Mathematics --- Statistical methods

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This book provides engineers and scientists in academia and industry with a thorough understanding of the underlying principles of nonlinear system identification. It equips them to apply the models and methods discussed to real problems with confidence, while also making them aware of potential difficulties that may arise in practice. Moreover, the book is self-contained, requiring only a basic grasp of matrix algebra, signals and systems, and statistics. Accordingly, it can also serve as an introduction to linear system identification, and provides a practical overview of the major optimization methods used in engineering. The focus is on gaining an intuitive understanding of the subject and the practical application of the techniques discussed. The book is not written in a theorem/proof style; instead, the mathematics is kept to a minimum, and the ideas covered are illustrated with numerous figures, examples, and real-world applications. In the past, nonlinear system identification was a field characterized by a variety of ad-hoc approaches, each applicable only to a very limited class of systems. With the advent of neural networks, fuzzy models, Gaussian process models, and modern structure optimization techniques, a much broader class of systems can now be handled. Although one major aspect of nonlinear systems is that virtually every one is unique, tools have since been developed that allow each approach to be applied to a wide variety of systems. .

Statistical physics. --- Control engineering. --- Robotics. --- Mechatronics. --- Computational complexity. --- Calculus of variations. --- Computer simulation. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Control and Systems Theory. --- Control, Robotics, Mechatronics. --- Complexity. --- Calculus of Variations and Optimal Control; Optimization. --- Simulation and Modeling. --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Physics --- Mathematical statistics --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Complexity, Computational --- Electronic data processing --- Machine theory --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Statistical methods --- System identification. --- Nonlinear systems. --- Automatic control engineering. --- Systems, Nonlinear --- System theory --- Identification, System --- System analysis