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Chaos --- Chaos

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Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications is a major reference for scientists and engineers interested in applying new computational and mathematical tools for solving complex problems related to modeling, analyzing and synchronizing chaotic systems. Furthermore, it offers an array of new, real-world applications in the field. Written by eminent scientists in the field of control theory and nonlinear systems from 19 countries (Cameroon, China, Ethiopia, France, Greece, India, Italia, Iran, Japan, Mexico, and more), this book covers the latest advances in chaos theory, along with the efficiency of novel synchronization approaches. Readers will find the fundamentals and algorithms related to the analysis and synchronization of chaotic systems, along with key applications, including electronic design, text and image encryption, and robot control and tracking.

Chaotic behavior in systems. --- Chaotic synchronization. --- Chaotic behavior in systems --- Synchronization --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory

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This book is primarily concerned with the computational aspects of predictability of dynamical systems - in particular those where observations, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, in astronomy it is uncommon to have the possibility of altering the key parameters of the studied objects. Therefore, the numerical simulations offer an essential tool for analysing these systems, and their reliability is of ever-increasing interest and importance. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation. This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the strong sensitivity to initial conditions and the use of Lyapunov exponents to characterize this sensitivity. This method is illustrated using several well-known continuous dynamical systems, such as the Contopoulos, Hénon-Heiles and Rössler systems. This second edition revises and significantly enlarges the material of the first edition by providing new entry points for discussing new predictability issues on a variety of areas such as machine decision-making, partial differential equations or the analysis of attractors and basins. Finally, the parts of the book devoted to the application of these ideas to astronomy have been greatly enlarged, by first presenting some basics aspects of predictability in astronomy and then by expanding these ideas to a detailed analysis of a galactic potential.

Chaotic behavior in systems --- Mathematical models. --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Statistical physics. --- Physics. --- Space sciences. --- Mathematical physics. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Numerical and Computational Physics, Simulation. --- Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics). --- Mathematical Applications in the Physical Sciences. --- Physical mathematics --- Physics --- Science and space --- Space research --- Cosmology --- Science --- Astronomy --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Mathematical statistics --- Mathematics --- Statistical methods

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Mathematics --- Classical mechanics. Field theory --- Statistical physics --- Electrical engineering --- Applied physical engineering --- Engineering sciences. Technology --- chaos --- toegepaste wiskunde --- theoretische fysica --- automatisering --- economie --- systeemtheorie --- wiskunde --- systeembeheer --- ingenieurswetenschappen --- dynamica

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Partial differential equations --- Differential equations --- Mathematics --- Classical mechanics. Field theory --- Statistical physics --- Applied physical engineering --- Computer science --- differentiaalvergelijkingen --- chaos --- toegepaste wiskunde --- theoretische fysica --- economie --- informatica --- wiskunde --- ingenieurswetenschappen --- dynamica