Aging transition in coupled quantum oscillators

Aging transition is an emergent behavior observed in networks consisting of active (self-oscillatory) and inactive (non self-oscillatory) nodes, where the network transits from a global oscillatory state to an oscillation collapsed state when the fraction of inactive oscillators surpasses a critical value. However, the aging transition in quantum domain has not been studied yet. In this paper we investigate the quantum manifestation of aging transition in a network of active-inactive quantum oscillators. We show that, unlike classical case, the quantum aging is not characterized by a complete collapse of oscillation but by sufficient reduction in the mean boson number. We identify a critical ``knee" value in the fraction of inactive oscillators around which quantum aging occurs in two different ways. Further, in stark contrast to the classical case, quantum aging transition depends upon the nonlinear damping parameter. We also explain the underlying processes leading to quantum aging that have no counterpart in the classical domain.Comment: Comments are welcom

The Kuramoto model in complex networks

181 pages, 48 figures. In Press, Accepted Manuscript, Physics Reports 2015 Acknowledgments We are indebted with B. Sonnenschein, E. R. dos Santos, P. Schultz, C. Grabow, M. Ha and C. Choi for insightful and helpful discussions. T.P. acknowledges FAPESP (No. 2012/22160-7 and No. 2015/02486-3) and IRTG 1740. P.J. thanks founding from the China Scholarship Council (CSC). F.A.R. acknowledges CNPq (Grant No. 305940/2010-4) and FAPESP (Grants No. 2011/50761-2 and No. 2013/26416-9) for financial support. J.K. would like to acknowledge IRTG 1740 (DFG and FAPESP).Peer reviewedPreprin

Adaptive Fuzzy Tracking Control with Global Prescribed-Time Prescribed Performance for Uncertain Strict-Feedback Nonlinear Systems

Adaptive fuzzy control strategies are established to achieve global prescribed performance with prescribed-time convergence for strict-feedback systems with mismatched uncertainties and unknown nonlinearities. Firstly, to quantify the transient and steady performance constraints of the tracking error, a class of prescribed-time prescribed performance functions are designed, and a novel error transformation function is introduced to remove the initial value constraints and solve the singularity problem in existing works. Secondly, based on dynamic surface control methods, controllers with or without approximating structures are established to guarantee that the tracking error achieves prescribed transient performance and converges into a prescribed bounded set within prescribed time. In particular, the settling time and initial value of the prescribed performance function are completely independent of initial conditions of the tracking error and system parameters, which improves existing results. Moreover, with a novel Lyapunov-like energy function, not only the differential explosion problem frequently occurring in backstepping techniques is solved, but the drawback of the semi-global boundedness of tracking error induced by dynamic surface control can be overcome. The validity and effectiveness of the main results are verified by numerical simulations on practical examples

Design and Development of a Twisted String Exoskeleton Robot for the Upper Limb

High-intensity and task-specific upper-limb treatment of active, highly repetitive movements are the effective approaches for patients with motor disorders. However, with the severe shortage of medical service in the United States and the fact that post-stroke survivors can continue to incur significant financial costs, patients often choose not to return to the hospital or clinic for complete recovery. Therefore, robot-assisted therapy can be considered as an alternative rehabilitation approach because the similar or better results as the patients who receive intensive conventional therapy offered by professional physicians.;The primary objective of this study was to design and fabricate an effective mobile assistive robotic system that can provide stroke patients shoulder and elbow assistance. To reduce the size of actuators and to minimize the weight that needs to be carried by users, two sets of dual twisted-string actuators, each with 7 strands (1 neutral and 6 effective) were used to extend/contract the adopted strings to drive the rotational movements of shoulder and elbow joints through a Bowden cable mechanism. Furthermore, movements of non-disabled people were captured as templates of training trajectories to provide effective rehabilitation.;The specific aims of this study included the development of a two-degree-of-freedom prototype for the elbow and shoulder joints, an adaptive robust control algorithm with cross-coupling dynamics that can compensate for both nonlinear factors of the system and asynchronization between individual actuators as well as an approach for extracting the reference trajectories for the assistive robotic from non-disabled people based on Microsoft Kinect sensor and Dynamic time warping algorithm. Finally, the data acquisition and control system of the robot was implemented by Intel Galileo and XILINX FPGA embedded system

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Synchronization of Coupled and Periodically Forced Chemical Oscillators

Physiological rhythms are essential in all living organisms. Such rhythms are regulated through the interactions of many cells. Deviation of a biological system from its normal rhythms can lead to physiological maladies. The tremor and symptoms associated with Parkinson\u27s disease are thought to emerge from abnormal synchrony of neuronal activity within the neural network of the brain. Deep brain stimulation is a therapeutic technique that can remove this pathological synchronization by the application of a periodic desynchronizing signal. Herein, we used the photosensitive Belousov--Zhabotinsky (BZ) chemical reaction to test the mechanism of deep brain stimulation. A collection of oscillators are initially synchronized using a regular light signal. Desynchronization is then attempted using an appropriately chosen desynchronizing signal based on information found in the phase response curve.;Coupled oscillators in various network topologies form the most common prototypical systems for studying networks of dynamical elements. In the present study, we couple discrete BZ photochemical oscillators in a network configuration. Different behaviors are observed on varying the coupling strength and the frequency heterogeneity, including incoherent oscillations to partial and full frequency entrainment. Phase clusters are organized symmetrically or non-symmetrically in phase-lag synchronization structures, a novel phase wave entrainment behavior in non-continuous media. The behavior is observed over a range of moderate coupling strengths and a broad frequency distribution of the oscillators

Coupling Functions:Dynamical Interaction Mechanisms in the Physical, Biological and Social Sciences

Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterised by coupling functions -- which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarises earlier work on coupling functions, reviews recent developments, presents the state-of-the-art, and looks forward to guide the future evolution of the field

Synchronization of coupled oscillators

Tese de mestrado em Física (Física Estatística e Não Linear), apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2010In this work we begin by introducing the Kuramoto model, constructing its solutions in the thermodynamic limit and showing the close connection between statistical physics and dynamical systems that lead to the main theoretical insights. The systematic study of a finite population of self sustained oscillators began in the first decade of this century. Unlike most of the papers we have found, we are not interested in the synchronization transition in itself but rather in phase locked patterns and their relation with frequency distribution among oscillators. The problem of stability, as we have already mentioned, experienced great advances in recent years. In a brief discussion we only address the problem of stability of the simplest solution allowed by the Kuramoto model: the incoherent solution. After that we introduce chimera states, first noticed by Kuramoto and his colleagues ([17] and references therein), in which the introduction of a non local coupling gives origin to a split in a region with synchronised oscillators and other with asynchronous one. Then we proceed by exploring the literature and the results with a finite number of oscillators, field explored with persistence only since mainly 2004 [29]. But here we are yet in Kuramoto framework which is abandoned, in a rigorous terminology, when we pursuit structured and not all-to-all coupling. Although we could introduce the same mean fields quantities if well defined in each situation, this did not help us in making sense of the results and is not an help in any analytical work. In our analysis of a ring of coupled oscillators we construct a space that allows us to relate the stable solutions with the eigenvectors of the laplacian of the graph in which we work.Neste trabalho começamos por introduzir o modelo de Kuramoto e realizar a construção das suas soluções no limite termodinâmico, mostrando a relação estreita entre física estatística e sistemas dinâmicos que levaram aos desenvolvimentos mais significativos. O estudo sistemático das populações de osciladores com um número finito de elementos começaram na primeira década deste século. Ao contrário de muitos trabalhos nesta área, não estamos interessados no processo de sincronização em si mas antes em padrões de fases que surgem em sincronia e sua relação com a distribuição das frequências próprias entre osciladores. O problema da estabilidade das soluções teve grandes desenvolvimento nos últimos anos. Numa breve análise apenas atendemos ao problema da estabilidade da mais simples solução do modelo de kuramoto: a solução incoerente. Depois introduzimos as quimeras, estados de sincronização descobertos por Kuramoto e que resultam da introdução de acoplamento não local, resultando numa separação entre uma zona de sincronia e uma zona assíncrona num mesmo sistema. Prosseguimos analisando a literatura e os resultados conhecidos com um número finito de osciladores, um campo explorado de forma sistemática apenas após, grosso modo, 2004. Abandonamos o modelo de Kuramoto quando passamos ao estudo de um número finito de osciladores e introduzimos acoplamentos estruturados saindo do acoplamento de todos com todos. Nesta situação as quantidades de campo médio, na origem do êxito do modelo de Kuramoto, ficam sem utilidade evidente, ainda que caso a caso se possam ainda definir e trabalhar. A nossa análise num círculo onde os osciladores acoplam entre primeiros vizinhos e construímos um espaço onde podemos visualizar a relação entre as soluções estáveis e os vectores próprios do operador Laplaciano do grafo associado