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The focus of this thesis are synchronization phenomena in networks and their intrinsic control through time delay, which is ubiquitous in real-world systems ranging from physics and acoustics to neuroscience and engineering. We encounter synchronization everywhere and it can be either a helpful or a detrimental mechanism. In the first part, after a survey of complex nonlinear systems and networks, we show that a seemingly simple system of two organ pipes gives birth to complex bifurcation and synchronization scenarios. Going from a 2-oscillator system to a ring of oscillators, we encounter the intriguing phenomenon of chimera states which are partial synchrony patterns with coexisting domains of synchronized and desynchronized dynamics. For more than a decade scientist have tried to solve the puzzle of this spontaneous symmetry-breaking emerging in networks of identical elements. We provide an analysis of initial conditions and extend our model by the addition of time delay and fractal connectivities. In the second part, we investigate partial synchronization patterns in a neuronal network and explain dynamical asymmetry arising from the hemispheric structure of the human brain. A particular focus is on the novel scenario of partial relay synchronization in multiplex networks. Such networks allow for synchronization of the coherent domains of chimera states via a remote layer, whereas the incoherent domains remain desynchronized. The theoretical framework is demonstrated with different generic models.
The focus of this thesis is the interplay of synchrony and adaptivity in complex networks. Synchronization is a ubiquitous phenomenon observed in different contexts in physics, chemistry, biology, neuroscience, medicine, socioeconomic systems, and engineering. Most prominently, synchronization takes place in the brain, where it is associated with cognitive capacities like learning and memory, but is also a characteristic of neurological diseases like Parkinson and epilepsy. Adaptivity is common in many networks in nature and technology, where the connectivity changes in time, i.e., the strength of the coupling is continuously adjusted depending upon the dynamic state of the system, for instance synaptic neuronal plasticity in the brain. This research contributes to a fundamental understanding of various synchronization patterns, including hierarchical multifrequency clusters, chimeras and other partial synchronization states. After a concise survey of the fundamentals of adaptive and complex dynamical networks and synaptic plasticity, in the first part of the thesis the existence and stability of cluster synchronization in globally coupled adaptive networks is discussed for simple paradigmatic phase oscillators as well as for a more realistic neuronal oscillator model with spike-timing dependent plasticity. In the second part of the thesis the interplay of adaptivity and connectivity is investigated for more complex network structures like nonlocally coupled rings, random networks, and multilayer systems. Besides presenting a plethora of novel, sometimes intriguing patterns of synchrony, the thesis makes a number of pioneering methodological advances, where rigorous mathematical proofs are given in the Appendices. These results are of interest not only from a fundamental point of view, but also with respect to challenging applications in neuroscience and technological systems.
This research aims to achieve a fundamental understanding of synchronization and its interplay with the topology of complex networks. Synchronization is a ubiquitous phenomenon observed in different contexts in physics, chemistry, biology, medicine and engineering. Most prominently, synchronization takes place in the brain, where it is associated with several cognitive capacities but is - in abundance - a characteristic of neurological diseases. Besides zero-lag synchrony, group and cluster states are considered, enabling a description and study of complex synchronization patterns within the presented theory. Adaptive control methods are developed, which allow the control of synchronization in scenarios where parameters drift or are unknown. These methods are, therefore, of particular interest for experimental setups or technological applications. The theoretical framework is demonstrated on generic models, coupled chemical oscillators and several detailed examples of neural networks.
This book introduces recent results on output synchronization of complex dynamical networks with single and multiple weights. It discusses novel research ideas and a number of definitions in complex dynamical networks, such as H-Infinity output synchronization, adaptive coupling weights, multiple weights, the relationship between output strict passivity and output synchronization. Furthermore, it methodically edits the research results previously published in various flagship journals and presents them in a unified form. The book is of interest to university researchers and graduate students in engineering and mathematics who wish to study output synchronization of complex dynamical networks.
This monograph studies the synchronization control of Markovian complex neural networks with time-varying delays, and the structure of the book is summarized as follows. Chapter 1 introduces the system description and some background knowledges, and also addresses the motivations of this monograph. In Chapter 2, the stochastic synchronization issue of Markovian coupled neural networks with partially unknown transition rates and random coupling strengths is investigated. In Chapter 3, the local synchronization issue of Markovian neutral complex networks with partially information of transition rates is investigated. The new delay-dependent synchronization criteria in terms of LMIs are derived, which depends on the upper and lower bounds of the delays. In Chapter 4, the local synchronization issue of Markovian nonlinear coupled neural networks with uncertain and partially unknown transition rates is investigated. The less conservative local synchronization criteria containing the bounds of delay and delay derivative are obtained based on the novel augmented Lyapunov-Krasovskii functional and a new integral inequality. In Chapter 5, the sampled-data synchronization issue of delayed complex networks with aperiodic sampling interval is investigated based on enhanced input delay approach, which makes full use of the upper bound of the variable sampling interval and the sawtooth structure information of varying input delay. In Chapter 6, the sampled-data synchronization issue of Markovian coupled neural networks with mode-dependent interval time-varying delays and aperiodic sampling intervals is investigated based on an enhanced input delay approach. Furthermore, the mode-dependent sampled-data controllers are proposed based on the delay dependent synchronization criteria. In Chapter 7, the synchronization issue of inertial neural networks with time-varying delays and generally Markovian jumping is investigated. In Chapter 8, we conclude the monograph by briefly summarizing the main theoretical findings.
Proceedings of the 49th Session of the International Seminars on Nuclear War and Planetary Emergencies held in Erice, Sicily. This Seminar has again gathered, in 2016, over one hundred scientists from 43 countries in an interdisciplinary effort that has been going on for the last 33 years, to examine and analyze planetary problems which had been followed up, all year long, by the World Federation of Scientists' Permanent Monitoring Panels.
This book establishes a unified framework for dealing with typical engineering complications arising in modern, complex, large-scale networks such as parameter uncertainties, missing measurement and cyber-attack. Distributed Filtering, Control and Synchronization is a timely reflection on methods designed to handle a series of control and signal-processing issues in modern industrial engineering practice in areas like power grids and environmental monitoring. It exploits the latest techniques to handle the emerging mathematical and computational challenges arising from, among other things, the dynamic topologies of distributed systems and in the context of sensor networks and multi-agent systems. These techniques include recursive linear matrix inequalities, local-performance and stochastic analyses and techniques based on matrix theory. Readers interested in the theory and application of control and signal processing will find much to interest them in the new models and methods presented in this book. Academic researchers can find ideas for developing their own research, graduate and advanced undergraduate students will be made aware of the state of the art, and practicing engineers will find methods for addressing practical difficulties besetting modern networked systems
This book focuses on the stability of the dynamical neural system, synchronization of the coupling neural system and their applications in automation control and electrical engineering. The redefined concept of stability, synchronization and consensus are adopted to provide a better explanation of the complex neural network. Researchers in the fields of dynamical systems, computer science, electrical engineering and mathematics will benefit from the discussions on complex systems. The book will also help readers to better understand the theory behind the control technique and its design.
This book introduces selected recent findings on the analysis and control of dynamical behaviors for coupled reaction-diffusion neural networks. It presents novel research ideas and essential definitions concerning coupled reaction-diffusion neural networks, such as passivity, adaptive coupling, spatial diffusion coupling, and the relationship between synchronization and output strict passivity. Further, it gathers research results previously published in many flagship journals, presenting them in a unified form. As such, the book will be of interest to all university researchers and graduate students in Engineering and Mathematics who wish to study the dynamical behaviors of coupled reaction-diffusion neural networks.