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In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.

n/a --- nonautonomous (autonomous) dynamical system --- stabilization --- multi-time scale fractional stochastic differential equations --- conditional Tsallis entropy --- wavelet transform --- hyperchaotic system --- Chua’s system --- permutation entropy --- neural network method --- Information transfer --- self-synchronous stream cipher --- colored noise --- Benettin method --- method of synchronization --- topological entropy --- geometric nonlinearity --- Kantz method --- dynamical system --- Gaussian white noise --- phase-locked loop --- wavelets --- Rosenstein method --- m-dimensional manifold --- deterministic chaos --- disturbation --- Mittag–Leffler function --- approximate entropy --- bounded chaos --- Adomian decomposition --- fractional calculus --- product MV-algebra --- Tsallis entropy --- descriptor fractional linear systems --- analytical solution --- fractional Brownian motion --- true chaos --- discrete mapping --- partition --- unbounded chaos --- fractional stochastic partial differential equation --- noise induced transitions --- random number generator --- Fourier spectrum --- hidden attractors --- (asymptotical) focal entropy point --- regular pencils --- continuous flow --- Bernoulli–Euler beam --- image encryption --- Gauss wavelets --- Lyapunov exponents --- discrete fractional calculus --- Lorenz system --- Schur factorization --- discrete chaos --- Wolf method

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This book presents recent developments in nonlinear and complex systems. It provides recent theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers information theory, relativistic chaotic dynamics, data analysis, relativistic chaotic dynamics, solvability issues in integro-differential equations, and inverse problems for parabolic differential equations, synchronization and chaotic transient. Presents new concepts for understanding and modeling complex systems.

Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- Applied physical engineering --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- neuronale netwerken --- fuzzy logic --- ICT (informatie- en communicatietechnieken) --- cybernetica --- economie --- wiskunde --- KI (kunstmatige intelligentie) --- ingenieurswetenschappen --- fysica --- dynamica

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In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Fractional calculus. --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus --- Engineering mathematics. --- Computer simulation. --- System theory. --- Mechanical engineering. --- Computer engineering. --- Mathematical and Computational Engineering. --- Simulation and Modeling. --- Systems Theory, Control. --- Theoretical, Mathematical and Computational Physics. --- Mechanical Engineering. --- Electrical Engineering. --- Systems, Theory of --- Systems science --- Science --- Computers --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Engineering analysis --- Philosophy --- Design and construction --- Mathematics --- Systems theory. --- Applied mathematics. --- Mathematical physics. --- Electrical engineering. --- Electric engineering --- Physical mathematics --- Physics

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Nonlinear systems --- Mathematical models. --- Systems, Nonlinear --- System theory --- System theory. --- Mathematics. --- Nonlinear systems. --- Math --- Science --- Systems, Theory of --- Systems science --- Philosophy

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This first of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to Nonlinear Dynamics of Structures, Systems and Devices. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume I include multi-scale dynamics: coexistence of multiple time/space scales, large system dynamics; dynamics of structures/industrial machines/equipment/facilities (e.g., cable transportation systems, suspension bridges, cranes, vehicles); nonlinear interactions: parametric vibrations with single/multi-frequency excitations, multiple external and autoparametric resonances in multi-dof systems; nonlinear system identification: parametric/nonparametric identification, data-driven identification; experimental dynamics: benchmark experiments, experimental methods, instrumentation techniques, measurements in harsh environments, experimental validation of nonlinear models; wave propagation, solitons, kinks, breathers; solution methods for pdes: Lie groups, Hirota’s method, perturbation methods, etc; nonlinear waves in media (granular materials, porous materials, materials with memory); composite structures: multi-layer, functionally graded, thermal loading; fluid/structure interaction; nonsmooth and retarded dynamics: systems with impacts, free play, stick-slip, friction hysteresis; nonlinear systems with time and/or space delays; stability of delay differential equations, differential-algebraic equations; space/time reduced-order modeling: enhanced discretization methods, center manifold reduction, nonlinear normal modes, normal forms; fractional-order systems; computational techniques: efficient algorithms, use of symbolic manipulators, integration of symbolic manipulation and numerical methods, use of parallel processors; and multibody dynamics: rigid and flexible multibody system dynamics, impact and contact mechanics, tire modeling, railroad vehicle dynamics, computational multibody dynamics.

Solid state physics. --- Mechanics. --- Mechanics, Applied. --- Statistical physics. --- Vibration. --- Dynamical systems. --- Dynamics. --- Computational complexity. --- Statics. --- Solid State Physics. --- Solid Mechanics. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Vibration, Dynamical Systems, Control. --- Complexity. --- Mechanical Statics and Structures. --- Engineering --- Mathematics --- Mechanics --- Mechanics, Analytic --- Physics --- Dynamics --- Equilibrium --- Complexity, Computational --- Electronic data processing --- Machine theory --- Dynamical systems --- Kinetics --- Force and energy --- Statics --- Cycles --- Sound --- Mathematical statistics --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Quantum theory --- Solids --- Statistical methods --- Nonlinear mechanics --- Condensed matter. --- Solids. --- Nonlinear Optics. --- Multibody systems. --- Nonlinear theories. --- Condensed Matter Physics. --- Multibody Systems and Mechanical Vibrations. --- Applied Dynamical Systems. --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Multi-body systems --- Systems, Multibody --- Optics, Nonlinear --- Optics --- Lasers --- Solid state physics --- Transparent solids --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter