2,317 research outputs found
Conditions for synchronizability in arrays of coupled linear systems
Synchronization control in arrays of identical output-coupled continuous-time
linear systems is studied. Sufficiency of new conditions for the existence of a
synchronizing feedback law are analyzed. It is shown that for neutrally stable
systems that are detectable form their outputs, a linear feedback law exists
under which any number of coupled systems synchronize provided that the
(directed, weighted) graph describing the interconnection is fixed and
connected. An algorithm generating one such feedback law is presented. It is
also shown that for critically unstable systems detectability is not
sufficient, whereas full-state coupling is, for the existence of a linear
feedback law that is synchronizing for all connected coupling configurations
Synchrony and bifurcations in coupled dynamical systems and effects of time delay
Dynamik auf Netzwerken ist ein mathematisches Feld, das in den letzten Jahrzehnten schnell gewachsen ist und Anwendungen in zahlreichen Disziplinen wie z.B. Physik, Biologie und Soziologie findet. Die Funktion vieler Netzwerke hängt von der Fähigkeit ab, die Elemente des Netzwerkes zu synchronisieren. Mit anderen Worten, die Existenz und die transversale Stabilität der synchronen Mannigfaltigkeit sind zentrale Eigenschaften. Erst seit einigen Jahren wird versucht, den verwickelten Zusammenhang zwischen der Kopplungsstruktur und den Stabilitätseigenschaften synchroner Zustände zu verstehen. Genau das ist das zentrale Thema dieser Arbeit. Zunächst präsentiere ich erste Ergebnisse zur Klassifizierung der Kanten eines gerichteten Netzwerks bezüglich ihrer Bedeutung für die Stabilität des synchronen Zustands. Folgend untersuche ich ein komplexes Verzweigungsszenario in einem gerichteten Ring von Stuart-Landau Oszillatoren und zeige, dass das Szenario persistent ist, wenn dem Netzwerk eine schwach gewichtete Kante hinzugefügt wird. Daraufhin untersuche ich synchrone Zustände in Ringen von Phasenoszillatoren die mit Zeitverzögerung gekoppelt sind. Ich bespreche die Koexistenz synchroner Lösungen und analysiere deren Stabilität und Verzweigungen. Weiter zeige ich, dass eine Zeitverschiebung genutzt werden kann, um Muster im Ring zu speichern und wiederzuerkennen. Diese Zeitverschiebung untersuche ich daraufhin für beliebige Kopplungsstrukturen. Ich zeige, dass invariante Mannigfaltigkeiten des Flusses sowie ihre Stabilität unter der Zeitverschiebung erhalten bleiben. Darüber hinaus bestimme ich die minimale Anzahl von Zeitverzögerungen, die gebraucht werden, um das System äquivalent zu beschreiben. Schließlich untersuche ich das auffällige Phänomen eines nichtstetigen Übergangs zu Synchronizität in Klassen großer Zufallsnetzwerke indem ich einen kürzlich eingeführten Zugang zur Beschreibung großer Zufallsnetzwerke auf den Fall zeitverzögerter Kopplungen verallgemeinere.Since a couple of decades, dynamics on networks is a rapidly growing branch of mathematics with applications in various disciplines such as physics, biology or sociology. The functioning of many networks heavily relies on the ability to synchronize the network’s nodes. More precisely, the existence and the transverse stability of the synchronous manifold are essential properties. It was only in the last few years that people tried to understand the entangled relation between the coupling structure of a network, given by a (di-)graph, and the stability properties of synchronous states. This is the central theme of this dissertation. I first present results towards a classification of the links in a directed, diffusive network according to their impact on the stability of synchronization. Then I investigate a complex bifurcation scenario observed in a directed ring of Stuart-Landau oscillators. I show that under the addition of a single weak link, this scenario is persistent. Subsequently, I investigate synchronous patterns in a directed ring of phase oscillators coupled with time delay. I discuss the coexistence of multiple of synchronous solutions and investigate their stability and bifurcations. I apply these results by showing that a certain time-shift transformation can be used in order to employ the ring as a pattern recognition device. Next, I investigate the same time-shift transformation for arbitrary coupling structures in a very general setting. I show that invariant manifolds of the flow together with their stability properties are conserved under the time-shift transformation. Furthermore, I determine the minimal number of delays needed to equivalently describe the system’s dynamics. Finally, I investigate a peculiar phenomenon of non-continuous transition to synchrony observed in certain classes of large random networks, generalizing a recently introduced approach for the description of large random networks to the case of delayed couplings
Non-Equilibrium Steady States for Networks of Oscillators
Non-equilibrium steady states for chains of oscillators (masses) connected by
harmonic and anharmonic springs and interacting with heat baths at different
temperatures have been the subject of several studies. In this paper, we show
how some of the results extend to more complicated networks. We establish the
existence and uniqueness of the non-equilibrium steady state, and show that the
system converges to it at an exponential rate. The arguments are based on
controllability and conditions on the potentials at infinity
Fracton pairing mechanism for "strange" superconductors: Self-assembling organic polymers and copper-oxide compounds
Self-assembling organic polymers and copper-oxide compounds are two classes
of "strange" superconductors, whose challenging behavior does not comply with
the traditional picture of Bardeen, Cooper, and Schrieffer (BCS)
superconductivity in regular crystals. In this paper, we propose a theoretical
model that accounts for the strange superconducting properties of either class
of the materials. These properties are considered as interconnected
manifestations of the same phenomenon: We argue that superconductivity occurs
in the both cases because the charge carriers (i.e., electrons or holes)
exchange {\it fracton excitations}, quantum oscillations of fractal lattices
that mimic the complex microscopic organization of the strange superconductors.
For the copper oxides, the superconducting transition temperature as
predicted by the fracton mechanism is of the order of K. We suggest
that the marginal ingredient of the high-temperature superconducting phase is
provided by fracton coupled holes that condensate in the conducting
copper-oxygen planes owing to the intrinsic field-effect-transistor
configuration of the cuprate compounds. For the gate-induced superconducting
phase in the electron-doped polymers, we simultaneously find a rather modest
transition temperature of K owing to the limitations imposed by
the electron tunneling processes on a fractal geometry. We speculate that
hole-type superconductivity observes larger onset temperatures when compared to
its electron-type counterpart. This promises an intriguing possibility of the
high-temperature superconducting states in hole-doped complex materials. A
specific prediction of the present study is universality of ac conduction for
.Comment: 12 pages (including separate abstract page), no figure
Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation
We present a detailed study of the effect of time delay on the collective
dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple
model consisting of just two oscillators with a time delayed coupling, the
bifurcation diagram obtained by numerical and analytical solutions shows
significant changes in the stability boundaries of the amplitude death, phase
locked and incoherent regions. A novel result is the occurrence of amplitude
death even in the absence of a frequency mismatch between the two oscillators.
Similar results are obtained for an array of N oscillators with a delayed mean
field coupling and the regions of such amplitude death in the parameter space
of the coupling strength and time delay are quantified. Some general analytic
results for the N tending to infinity (thermodynamic) limit are also obtained
and the implications of the time delay effects for physical applications are
discussed.Comment: 20 aps formatted revtex pages (including 13 PS figures); Minor
changes over the previous version; To be published in Physica
Robust Observation and Control of Complex Networks
The problem of understanding when individual actions of interacting agents display to a coordinated collective behavior has receiving a considerable attention in many research fields. Especially in control engineering, distributed applications in cooperative environments
are achieving resounding success, due to the large number of relevant applications, such as formation control, attitude synchronization tasks and cooperative applications in large-scale systems.
Although those problems have been extensively studied in Literature, themost of classic approaches use to consider the unrealistic scenario in which networks always consist of
identical, linear, time-invariant entities. It’s clear that this assumption strongly approximates the effective behavior of a network. In fact agents can be subjected to parameter uncertainties,
unmodeled dynamics or simply characterized by proper nonlinear dynamics.
Therefore, motivated by those practical problems, the present Thesis proposes various approaches for dealing with the problem of observation and control in both the framework
of multi-agents and complex interconnected systems. The main contributions of this Thesis consist on the development of several algorithms based on concepts of discontinuous slidingmode control. This techniques can be employed for solving in finite-time problems of robust
state estimation and consensus-based synchronization in network of heterogenous nonlinear systems subjected to unknown but bounded disturbances and sudden topological changes.
Both directed and undirected topologies have been taken into account. It is worth to mention also the extension of the consensus problem to networks of agents governed by a class parabolic partial differential equation, for which, for the first time, a boundary-based robust local interaction protocol has been presented
Robust Observation and Control of Complex Networks
The problem of understanding when individual actions of interacting agents display to a coordinated collective behavior has receiving a considerable attention in many research fields. Especially in control engineering, distributed applications in cooperative environments
are achieving resounding success, due to the large number of relevant applications, such as formation control, attitude synchronization tasks and cooperative applications in large-scale systems.
Although those problems have been extensively studied in Literature, themost of classic approaches use to consider the unrealistic scenario in which networks always consist of
identical, linear, time-invariant entities. It’s clear that this assumption strongly approximates the effective behavior of a network. In fact agents can be subjected to parameter uncertainties,
unmodeled dynamics or simply characterized by proper nonlinear dynamics.
Therefore, motivated by those practical problems, the present Thesis proposes various approaches for dealing with the problem of observation and control in both the framework
of multi-agents and complex interconnected systems. The main contributions of this Thesis consist on the development of several algorithms based on concepts of discontinuous slidingmode control. This techniques can be employed for solving in finite-time problems of robust
state estimation and consensus-based synchronization in network of heterogenous nonlinear systems subjected to unknown but bounded disturbances and sudden topological changes.
Both directed and undirected topologies have been taken into account. It is worth to mention also the extension of the consensus problem to networks of agents governed by a class parabolic partial differential equation, for which, for the first time, a boundary-based robust local interaction protocol has been presented
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