Long-range interaction induced collective dynamical behaviors

Sathiyadevi, K.; Chandrasekar, V. K.; Senthilkumar, D. V.; Lakshmanan, M.

doi:10.1088/1751-8121/ab111a

Cited by 20 publications

(11 citation statements)

References 64 publications

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“…Solitary states are described as states for which only one single element behaves differently compared with the behavior of the background group, i.e., the neighboring elements. These kinds of states have been observed in generalized Kuramoto-Sakaguchi models [MAI14a, WU18a, TEI19, CHE19b], the Kuramoto model with inertia [JAR15, JAR18], models of power grids [TAH19,HEL20], the Stuart-Landau model [SAT19], the FitzHugh-Nagumo model [RYB19a,SCH19a], systems of excitable units [ZAK16b] as well as in Lozi maps [RYB17] and even in experimental setups of coupled pendula [KAP14]. Solitary states are considered as important states in the transition from coherent to incoherent dynamics [JAR15,SEM15b,MIK18].…”

Section: Synchronization and Collective Phenomenamentioning

confidence: 99%

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Berner¹

2021

Springer Theses

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Collective phenomena in systems of interconnected dynamical units are omnipresent in nature. The swarm behavior in flocks of birds or schools of fish, the synchronous flashing of fireflies or even coherent spiking of neurons in the human brain are just a few examples of collective motion. Elucidating the mechanisms that give rise to synchronization is crucial in order to understand biological self-organization. For this sake, the theory of dynamical networks has been successfully applied over the last decades to boil down the complex dynamics from natural systems to their essentials. In addition, dynamical networks with adaptive couplings and hence non-constant network structure appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. In this thesis, we study adaptive networks and their properties which give rise to the emergence of a variety of synchronization patterns, including complete and cluster synchronization as well as solitary and chimera-like states. One of the main fields of application that is investigated in this thesis concerns neuroscience. However, the methods and approaches developed in this work are not restricted to a specific field of application.aus gekoppelten Phasenoszillatoren an und zeigen, wie das subtile Zusammenspiel zwischen Adaptivität und Netzwerkstruktur die Entstehung komplexer partieller Synchronisationsmuster hervorruft.Trotz des regen Interesses an adaptiven Netzwerken ist über das Zusammenspiel adaptiv gekoppelter Netzwerkgruppen wenig bekannt. Solche adaptiven Mehrschicht-oder Multiplex-Netzwerke kommen in neuronalen Netzwerken ganz natürlich vor. Wir schlagen ein Konzept zur Erzeugung und Stabilisierung diverser partieller Synchronisationsmuster (Phasen-Cluster) in adaptiven Netzwerken vor. Wir zeigen, dass das "Multiplexen" verschiedene stabile Phasen-Cluster-Zustände induzieren kann, selbst wenn diese in den Einschicht-Systemen nicht stabil sind oder gar nicht existieren. Weiterhin entwickeln wir eine Methode zur Analyse von Laplace-Matrizen von Multiplex-Netzwerken, die einen Einblick in die spektrale Struktur dieser Netzwerke ermöglicht und damit eine Reduktion des Stabilitätsproblems auf die von Einschicht-Netzwerken ermöglicht. Wir setzen die neue Methode ein, um analytische Ergebnisse für die Stabilität der Zustände im Mehrschicht-System zu erhalten.

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Section: Synchronization and Collective Phenomenamentioning

confidence: 99%

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Berner¹

2021

Springer Theses

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“…A generalized solitary state, where several oscillators exhibit dynamics different from that of the synchronous cluster received attention in Refs. [46][47][48][49][50][51][52][53][54][55] . This state appears at the border between synchrony and asynchrony, as soon as repulsion starts to prevail over attraction.…”

Section: Introductionmentioning

confidence: 99%

Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions

Teichmann

Rosenblum

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group are identical, but natural frequencies of the groups differ. In addition to a synchronous two-cluster state, the system exhibits a solitary state, when a single oscillator leaves the cluster of repulsive elements, as well as partially synchronous quasiperiodic dynamics. We demonstrate how the transitions between these states occur when the repulsion starts to prevail over attraction.PACS numbers: 05.45.Xt Synchronization; coupled oscillators Networks of coupled oscillators are a popular model for many engineered or natural systems. The main effect -emergence of a collective mode via synchronization -is now well-understood and therefore focus of research shifted recently to analysis of different complex states. These states include chimeras, when a population of identical units splits into a synchronous and asynchronous part, quasiperiodic partially synchronous states, characterized by the difference of frequencies of individual units and of the collective mode, and clusters and heteroclinic cycles, to name just a few. Of particular interest are ensembles where some elements have only attractive connections while others have only repulsive ones. This model is motivated by studies of neuronal networks that are built from excitatory and inhibitory neurons. In this paper we analyze how the state of such a setup changes with the interplay of attraction and repulsion. We demonstrate that if the frequency mismatch between attractive and repulsive units is smaller than some critical value then desynchronization occurs via appearance of the solitary state. With the further increase of repulsion the system undergoes a transition to quasiperiodic partial synchrony. In the latter state the attractive units remain synchronized, while the repulsive group settles between synchrony and asynchrony so that the mean fields of both groups remain locked, but the frequency of the repulsive elements is larger than that of their mean field. For a large frequency mismatch of attractive and repulsive groups desynchronization immediately leads to partial synchrony.

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“…The solitary state has also been found numerically in simulations of coupled Lorenz oscillators [46] and in a ring of coupled Stuart-Landau oscillators with symmetry breaking attractive and repulsive long-range coupling [47]. The observation of the existence in multiplex networks of FitzHugh-Nagumo oscillators coupled in rings with a small mismatch in the intra-layer couplings [48], allows even for controlling strategies to tune the dynamics in, e.g., neural networks.…”

Section: Weakly Coupled Oscillators-kuramoto Modelmentioning

confidence: 66%

Using phase dynamics to study partial synchrony: three examples

Teichmann

2021

Eur. Phys. J. Spec. Top.

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Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to analyze coupled oscillatory systems. Typically, the phase dynamics description is obtained in the weak coupling limit, i.e., in the first-order in the coupling strength. The extension beyond the first-order represents an unsolved problem and is an active area of research. In this paper, three partially synchronous states are investigated and presented in order of increasing complexity. First, the usage of the phase response curve for the description of macroscopic oscillators is analyzed. To achieve this, the response of the mean-field oscillations in a model of all-to-all coupled limit-cycle oscillators to pulse stimulation is measured. The next part treats a two-group Kuramoto model, where the interaction of one attractive and one repulsive group results in an interesting solitary state, situated between full synchrony and self-consistent partial synchrony. In the last part, the phase dynamics of a relatively simple system of three Stuart-Landau oscillators are extended beyond the weak coupling limit. The resulting model contains triplet terms in the high-order phase approximation, though the structural connections are only pairwise. Finally, the scaling of the new terms with the coupling is analyzed.

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Long-range interaction induced collective dynamical behaviors

Cited by 20 publications

References 64 publications

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions

Using phase dynamics to study partial synchrony: three examples

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