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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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System theory --- Dynamics. --- System theory. --- Mathematical models. --- Systems, Theory of --- Systems science --- Science --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Philosophy

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This book explores recent developments in theoretical research and mathematical modelling of real-world complex systems, organized in four parts. The first part of the book is devoted to the mathematical tools for the design and analysis in engineering and social science study cases. We discuss the periodic evolutions in nonlinear chemical processes, vibro-compact systems and their behaviour, different types of metal-semiconductor self-assembled samples, made of silver nanowires and zinc oxide nanorods. The second part of the book is devoted to mathematical description and modelling of the critical events, climate change and robust emergency scales. In three chapters, we consider a climate-economy model with endogenous carbon intensity and the behaviour of Tehran Stock Exchange market under international sanctions. The third part of the book is devoted to fractional dynamic and fractional control problems. We discuss the novel operational matrix technique for variable-order fractional optimal control problems, the nonlinear variable-order time fractional convection-diffusion equation with generalized polynomials The fourth part of the book concerns solvability and inverse problems in differential and integro-differential equations. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists and urban planners.

Discrete mathematics --- Mathematics --- Classical mechanics. Field theory --- toegepaste wiskunde --- grafentheorie --- systeemtheorie --- wiskunde --- dynamica

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This second of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to Nonlinear Dynamics and Control. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume II include influence of nonlinearities on vibration control systems; passive, semi-active, active control of structures and systems; synchronization; robotics and human-machine interaction; network dynamics control (multi-agent systems, leader-follower dynamics, swarm dynamics, biological networks dynamics); and fractional-order control.

Optics. --- Electrodynamics. --- Vibration. --- Dynamical systems. --- Dynamics. --- Control engineering. --- Statistical physics. --- Computational complexity. --- Classical Electrodynamics. --- Vibration, Dynamical Systems, Control. --- Control and Systems Theory. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Physics --- Mathematical statistics --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Cycles --- Sound --- Dynamics --- Light --- Statistical methods --- Nonlinear mechanics --- Automatic control.

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This book contains some of the contributions under ?ve main titles that are carefully selected according to the reports of referees, presented at the Int- national Symposium, MME06 Mathematical Methods in Engineering, held in C ¸ankaya University, Ankara, April 27-29, 2006. The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory. The members of the organizing committee were Dumitru Baleanu,Ronald A.DeVore,J.A.TenreiroMachado,AliH.NayfehandKenanTas(Chairman). Lecturersof the Symposium wereOm P. Agrawal,BrianFisher, J.A. Tenreiro Machado, Francesco Mainardi, Hans J. Stetter. The editors of this book are grateful to the President of the board of trusteesofC ¸ankayaUniversitySitkiAlp,totheRectorProf.Dr.ZiyaAkta¸sfor their continuous support of the Symposium activities. We are also obliged to the TUBITAK (The Scienti?c and TechnologicalResearchCouncilof Turkey) for their co-sponsorship. We would like to thank all the referees and other colleagues who helped in preparingthisbookforpublication.Ourthanksarealsoduetoallparticipants for their contributions to the Symposium and to this book. TheOrganizingCommitteewishestoexpresstheirthankstoProf.Dr.Emel Dogramaci, Dean of the Faculty of Arts and Science and to the colleagues of theDepartmentofMathematicsandComputerScienceofC ¸ankayaUniversity: A. Eris, F. Kumsel, M. Cenk, A. Bilgen, H. Baydar, Ozlem Defterli and A. Kabarcik who provided valuable work during the Symposium, and to our students: C. Acar, S. Arik, M.T. Dinc, K. Dogan, K.U. Aydin, R. Cebe, S. Ozsahin, B. Tasar, H. Hatipoglu, Y. Kaya, I.N. Ekim for their assistance.

Algebra --- Mathematics --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- algebra --- analyse (wiskunde) --- vormgeving --- functies (wiskunde) --- simulaties --- systeemtheorie --- wiskunde --- systeembeheer --- ingenieurswetenschappen