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Difference Equations and Their Applications
The theory of difference equations is now enjoying a period of Renaissance. Witness the large number of papers in which problems, having at first sight no common features, are reduced to the investigation of subsequent iterations of the maps f· IR. m ~ IR. m, m > 0, or (which is, in fact, the same) to difference equations The world of difference equations, which has been almost hidden up to now, begins to open in all its richness. Those experts, who usually use differential equations and, in fact, believe in their universality, are now discovering a completely new approach which re sembles the theory of ordinary differential equations only slightly. Difference equations, which reflect one o...
Control of Self-Organizing Nonlinear Systems
The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.
Dynamics of Complex Autonomous Boolean Networks
This thesis focuses on the dynamics of autonomous Boolean networks, on the basis of Boolean logic functions in continuous time without external clocking. These networks are realized with integrated circuits on an electronic chip as a field programmable gate array (FPGA) with roughly 100,000 logic gates, offering an extremely flexible model system. It allows fast and cheap design cycles and large networks with arbitrary topologies and coupling delays. The author presents pioneering results on theoretical modeling, experimental realization, and selected applications. In this regard, three classes of novel dynamic behavior are investigated: (i) Chaotic Boolean networks are proposed as high-spee...
Synchronization
Synchronization is a universal phenomenon that is encountered in nature, science and engineering. The book presents a broad view of modern theoretical and experimental approaches to synchronization, especially in complex and chaotic systems, and its applications in life sciences and engineering. Contributors include applied mathematicians, physicists, biologists, and specialists in communications and control theory. The study of synchronization is presented in its many aspects: basic mathematical theory, numerical simulation of complex systems, applications of methods in theoretical physics, experimental implementation, and applications in engineering and life sciences.
Lozi Mappings
This book is a comprehensive collection of known results about the Lozi map, a piecewise-affine version of the Henon map. Henon map is one of the most studied examples in dynamical systems and it attracts a lot of attention from researchers, however it is difficult to analyze analytically. Simpler structure of the Lozi map makes it more suitable fo
Synchronization and Waves in Active Media
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 verificat...
Energy Transmission and Synchronization in Complex Networks
This work tackles the problems of understanding how energy is transmitted and distributed in power-grids as well as in determining how robust this transmission and distribution is when modifications to the grid or power occur. The most important outcome is the derivation of explicit relationships between the structure of the grid, the optimal transmission and distribution of energy, and the grid’s collective behavior (namely, the synchronous generation of power). These relationships are extremely relevant for the design of resilient power-grid models. To allow the reader to apply these results to other complex systems, the thesis includes a review of relevant aspects of network theory, spectral theory, and novel analytical calculations to predict the existence and stability of periodic collective behavior in complex networks of phase oscillators, which constitute a paradigmatic model for many complex systems.
New Horizons in Millimeter-Wave, Infrared and Terahertz Technologies
This book presents recent and upcoming technological advancements in millimeter-wave (mm-wave), infrared (IR) and terahertz (THz) frequency spectrums. The scope of this book includes a significantly long portion of the electromagnetic spectrum, starting from the mm-waves (i.e. 30 GHz) and extended up to the end of the near-IR spectrum (i.e. 450 THz). Most significant aspect of this portion of the electromagnetic spectrum is that it includes a frequency regime where the gradual technological transition from electronics to photonics occurred. The book especially focuses on the recent advancements and several research issues related to materials, sources, detectors, passive circuits, advanced signal processing and image processing algorithms for mm-wave, IR and THz frequency bands. The book covers a very wide range of readers from basic science to technological experts as well as research scholars.
Piecewise-smooth Dynamical Systems
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.
