54 research outputs found
Swarmalators under competitive time-varying phase interactions
Swarmalators are entities with the simultaneous presence of swarming and
synchronization that reveal emergent collective behavior due to the fascinating
bidirectional interplay between phase and spatial dynamics. Although different
coupling topologies have already been considered, here we introduce
time-varying competitive phase interaction among swarmalators where the
underlying connectivity for attractive and repulsive coupling varies depending
on the vision (sensing) radius. Apart from investigating some fundamental
properties like conservation of center of position and collision avoidance, we
also scrutinize the cases of extreme limits of vision radius. The concurrence
of attractive-repulsive competitive phase coupling allows the exploration of
diverse asymptotic states, like static , and mixed phase wave states, and
we explore the feasible routes of those states through a detailed numerical
analysis. In sole presence of attractive local coupling, we reveal the
occurrence of static cluster synchronization where the number of clusters
depends crucially on the initial distribution of positions and phases of each
swarmalator. In addition, we analytically calculate the sufficient condition
for the emergence of the static synchronization state. We further report the
appearance of the static ring phase wave state and evaluate its radius
theoretically. Finally, we validate our findings using Stuart-Landau
oscillators to describe the phase dynamics of swarmalators subject to
attractive local coupling.Comment: 21 pages, 12 figures; accepted for publication in New Journal of
Physic
Synchronization in STDP-driven memristive neural networks with time-varying topology
Synchronization is a widespread phenomenon in the brain. Despite numerous
studies, the specific parameter configurations of the synaptic network
structure and learning rules needed to achieve robust and enduring
synchronization in neurons driven by spike-timing-dependent plasticity (STDP)
and temporal networks subject to homeostatic structural plasticity (HSP) rules
remain unclear. Here, we bridge this gap by determining the configurations
required to achieve high and stable degrees of complete synchronization (CS)
and phase synchronization (PS) in time-varying small-world and random neural
networks driven by STDP and HSP. In particular, we found that decreasing
(which enhances the strengthening effect of STDP on the average synaptic
weight) and increasing (which speeds up the swapping rate of synapses
between neurons) always lead to higher and more stable degrees of CS and PS in
small-world and random networks, provided that the network parameters such as
the synaptic time delay , the average degree , and
the rewiring probability have some appropriate values. When ,
, and are not fixed at these appropriate values, the
degree and stability of CS and PS may increase or decrease when increases,
depending on the network topology. It is also found that the time delay
can induce intermittent CS and PS whose occurrence is independent .
Our results could have applications in designing neuromorphic circuits for
optimal information processing and transmission via synchronization phenomena.Comment: 28 pages, 86 references, 8 figures, 2 Table
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
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
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