Oscillation quenching mechanisms: Amplitude vs. oscillation death

Koseska, Aneta; Volkov, E.I.; Kurths, Jürgen

doi:10.1016/j.physrep.2013.06.001

Cited by 378 publications

(321 citation statements)

References 117 publications

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“…Recently, special attention has been paid to the different types of oscillation quenching, amplitude death and oscillation death [13][14][15][16]. Amplitude death and oscillation death differ in the mechanisms by which they are induced: In coupled oscillator networks, the coupling between oscillators can stabilize an already existing homogeneous steady state which is unstable in the absence of coupling.…”

Section: Introductionmentioning

confidence: 99%

Stable and transient multicluster oscillation death in nonlocally coupled networks

et al. 2015

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In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multi-cluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations. To explain these phenomena analytically in dependence on the coupling range and the coupling strength, we first use a mean-field approximation which works well for large coupling ranges but fails for coupling ranges which are small compared to the cluster size. Going beyond standard mean-field theory, we predict the boundaries of the different stability regimes as well as the transient times analytically in excellent agreement with numerical results.

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Section: Introductionmentioning

confidence: 99%

Stable and transient multicluster oscillation death in nonlocally coupled networks

et al. 2015

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“…As an example, we have quenched the oscillations in a Stuart-Landau oscillator. Such an inhomogeneous steady state is known as oscillation death [Koseska et al, 2010[Koseska et al, , 2013aZakharova et al, 2013] and has been found in various systems including tunnel diodes [Heinrich et al, 2010], neuronal networks [Curtu, 2010], and genetic oscillators [Koseska et al, 2009]. This example demonstrates that we have found a very versatile method to construct networks that show a desired dynamical behavior.…”

Section: Resultsmentioning

confidence: 75%

Controlling Synchronization Patterns in Complex Networks

Lehnert¹

2016

Springer Theses

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In this thesis, I consider the control of synchronization in delay-coupled complex networks. As one main focus, several applications to neural networks will be discussed. In the first part, I focus on the stability of synchronization in complex networks meaning that the control is realized by considering the stability of synchrony in dependence on the parameters. In the second part, adaptive control of synchronization is studied. To this end, adaptive control algorithms are developed that tune the system parameters such that the desired control goal is reached.Besides zero-lag synchrony -a state where all nodes follow the same dynamics without a phase lag -groups and cluster states are considered, i.e., states where the network consists of several groups where the nodes within one group are in zero-lag synchrony and, in the case of cluster synchrony, with a constant phase lag between the clusters.The stability of synchronization can be accessed via the master stability function [Pecora and Carroll, 1998]. This convenient tool allows for treating the node dynamics and the network topology in two separate steps, and, thus, allows for a quite general treatment of different network topologies. In this thesis, I will discuss the generalization of the master stability function to group and cluster states and to non-smooth systems.The master stability function can be used to investigate synchrony in neural networks. Neurons are excitable systems where type-I and type-II excitability can be distinguished. Here, the stability of synchrony for both types in complex networks with excitatory and inhibitory links is investigated on two generic models, namely the normal form of the saddle-node infinite period bifurcation and the FitzHugh-Nagumo system. Furthermore, synchronization in systems with heterogeneous delays or node parameters is studied.In situations where parameters are unknown or drift, adaptive control methods are useful since they allow for an automatically realized adaption of the control parameters. A convenient adaptive method is the speed-gradient method that minimizes a predefined goal function [Fradkov, 1979[Fradkov, , 2007. I first apply this method in the control of an unstable focus and an unstable periodic orbit embedded in the Rössler attractor. Furthermore, I show that clusters states in networks of delayed coupled Stuart-Landau oscillators can be controlled by adaptively tuning the phase of the complex coupling strength or by adapting the topology. The first method is particularly simple because only one parameter has to be adapted, while the second method is more reliable in the sense that its success is widely independent of the choice of the control parameters and the initial conditions. ZUSAMMENFASSUNGIn dieser Arbeit wird die Kontrolle von Synchronisation in komplexen Netzwerken mit retardierten Kopplungen untersucht. Dabei werden verschiedene Anwendungen auf neuronale Netzwerke diskutiert. Der erste Teil der Arbeit beschäftigt sich mit der Stabilität von Synchronisation in komplexen Ne...

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“…Phase entrainment is not the only synchronization scenario. At the opposite pole, synchronization may quench oscillations [40] [45] [46] [47] [48], the phenomenon known also as amplitude death or oscillation cessation. Quenching scenario depends on the details of involved oscillators, their coupling mechanisms, and other conditions.…”

Section: Quantum Distributionsmentioning

confidence: 99%

An Emergence of a Quantum World in a Self-Organized Vacuum—A Possible Scenario

Manasson¹

2017

JMP

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We have explored a model of vacuum self-organization based on dissipative dynamics and recurrent self-interactions. The initial state of the vacuum is assumed as self-interacting vacuum dust. The medium is dispersive and resembles dark-energy vacuum as described by general relativity. Beside selfdiffusion, vacuum dust endowed with self-attraction, resembling Newton's gravity. We explored what would happen with this medium when the strength of self-gravitation progressively increases. We observed a cascade of phase transitions. First transition occurs when self-attraction reaches the point when it can balance self-diffusion. A vortex-cellular structure emerges. Vortexes operate as self-sustained oscillators and tend to synchronize their dynamics. They form a synchronized network that possesses a universal time scale and, after zooming out, its structure acquires a form of fiber-bundle structure of electromagnetic field. With increasing self-gravitation strength, the system experiences another phase transition. The fiber-bundle structure becomes resembling that of weak nuclear field. Vacuum cells acquire spinorial dynamics. Electric charges emerge. When synchronized, the weakly interacting cells create lepton-like molecules. Oscillating charges in spinorial cells give a birth to current loops, which magnetic moment linked to the particle spin. During the next phase transition, the cell dynamics experiences another topological transformation, which is accompanied by creation of three color charges. The acquired fiber-bundle structure form resembles that of strong nuclear field. Synchronized strongly interacting vacuum cells create quark-like particles that carry color charges. We associate their complex synchronization patterns with particle flavors. We also explored statistical distributions of vacuum cells as functions of self-gravitation strength. We found that the distribution spectrum is essentially discrete, and the vacuum cells group around the states that we call super-attractive. Discrete cell distribution implies charge quantization. Synchronization transforms initial Boltzmannlike distribution into quantum-like distributions. During phase transitions, cell distributions experience transformations that can be encoded in the

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Oscillation quenching mechanisms: Amplitude vs. oscillation death

Cited by 378 publications

References 117 publications

Stable and transient multicluster oscillation death in nonlocally coupled networks

Stable and transient multicluster oscillation death in nonlocally coupled networks

Controlling Synchronization Patterns in Complex Networks

An Emergence of a Quantum World in a Self-Organized Vacuum—A Possible Scenario

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