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The interplay between synchronization and spatio-temporal pattern formation is central for a broad variety of phenomena in nature, such as the coordinated contraction of heart tissue, associative memory and learning in neural networks, and pathological synchronization during Parkinson disease or epilepsy. In this thesis, three open puzzles of fundametal research in Nonlinear Dynamics are tackled: How does spatial confinement affect the dynamics of three-dimensional vortex rings? What role do permutation symmetries play in the spreading of excitation waves on networks? Does the spiral wave chimera state really exist? All investigations combine a theoretical approach and experimental verification, which exploit an oscillatory chemical reaction. A novel experimental setup is developed that allows for studying networks with N > 1000 neuromorphic relaxation oscillators. It facilitates the free choice of network topology, coupling function as well as its strength, range and time delay, which can even be chosen as time-dependent. These experimental capabilities open the door to a broad range of future experimental inquiries into pattern formation and synchronization on large networks, which were previously out of reach. .

Waves. --- Statistical physics. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Statistical Physics and Dynamical Systems. --- Biological and Medical Physics, Biophysics. --- Physics --- Mathematical statistics --- Statistical methods --- Biophysics. --- Biological physics. --- Biological physics --- Biology --- Medical sciences

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This book presents the most significant contributions to the DINAME 2017 conference, covering a range of dynamic problems to provide insights into recent trends and advances in a broad variety of fields seldom found in other proceedings volumes. DINAME has been held every two years since 1986 and is internationally recognized as a central forum for discussing scientific achievements related to dynamic problems in mechanics. Unlike many other conferences, it employs a single-session format for the oral presentations of all papers, which limits the number of accepted papers to roughly 100 and makes the evaluation process extremely rigorous. The papers gathered here will be of interest to all researchers, graduate students and engineering professionals working in the fields of mechanical and mechatronics engineering and related areas around the globe.

Mechanical engineering --- Vibration. --- Vibration, Dynamical Systems, Control. --- Control, Robotics, Mechatronics. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Cycles --- Mechanics --- Sound --- Dynamical systems. --- Dynamics. --- Control engineering. --- Robotics. --- Mechatronics. --- Statistical physics. --- Physics --- Mathematical statistics --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics --- Statistical methods

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This book collects recent developments in nonlinear and complex systems. It provides up-to-date 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 symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls. · Introduces new concepts for understanding and modeling complex systems; · Explains risk reduction management in complex systems; · Examines the symmetry group approach to understanding complex systems; · Illustrates the relation between transient chaos and crises.

Nonlinear systems. --- Engineering. --- Vibration. --- Complexity. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Mathematical Modeling and Industrial Mathematics. --- Vibration, Dynamical Systems, Control. --- Cycles --- Mechanics --- Sound --- Construction --- Industrial arts --- Technology --- Computational complexity. --- Statistical physics. --- Mathematical models. --- Dynamical systems. --- Dynamics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Models, Mathematical --- Simulation methods --- Mathematical statistics --- Complexity, Computational --- Electronic data processing --- Machine theory --- Statistical methods

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This book presents recent developments in nonlinear dynamics with an emphasis on complex systems. The volume illustrates new methods to characterize the solutions of nonlinear dynamics associated with complex systems. This book contains the following topics: new solutions of the functional equations, optimization algorithm for traveling salesman problem, fractals, control, fractional calculus models, fractional discretization, local fractional partial differential equations and their applications, and solutions of fractional kinetic equations.

Engineering mathematics --- Engineering. --- Complexity. --- Complex Systems. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Construction --- Industrial arts --- Technology --- Computational complexity. --- System theory. --- Statistical physics. --- Physics --- Mathematical statistics --- Systems, Theory of --- Systems science --- Science --- Complexity, Computational --- Electronic data processing --- Machine theory --- Statistical methods --- Philosophy

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This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.

Engineering mathematics. --- Systems theory. --- Engineering Mathematics. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Control and Systems Theory. --- Systems Theory, Control. --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Statistical physics. --- Control engineering. --- System theory. --- Physics --- Mathematical statistics --- Systems, Theory of --- Systems science --- Science --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Statistical methods --- Philosophy