Synchronization in networks of spatially extended systems

Filatova, Anastasiya; Hramov, Alexander E.; Короновский, А. А.; Boccaletti, Stefano

doi:10.1063/1.2940685

Cited by 19 publications

(15 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Potential applications of chimera states in nature include the phenomenon of unihemispheric sleep in birds and dolphins [24], bump states in neural systems [25,26], in power grids [27], or in social systems [28]. Many works * corresponding author: omelchenko@itp.tu-berlin.de considering chimera states were mostly based on numerical results.…”

Section: Introductionmentioning

confidence: 99%

Robustness of chimera states for coupled FitzHugh-Nagumo oscillators

et al. 2015

View full text Add to dashboard Cite

Chimera states are complex spatio-temporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics. This counterintuitive phenomenon was first observed in systems of identical oscillators with symmetric coupling topology. Can one overcome these limitations? To address this question, we discuss the robustness of chimera states in networks of FitzHugh-Nagumo oscillators. Considering networks of inhomogeneous elements with regular coupling topology, and networks of identical elements with irregular coupling topologies, we demonstrate that chimera states are robust with respect to these perturbations and analyze their properties as the inhomogeneities increase. We find that modifications of coupling topologies cause qualitative changes of chimera states: additional random links induce a shift of the stability regions in the system parameter plane, gaps in the connectivity matrix result in a change of the multiplicity of incoherent regions of the chimera state, and hierarchical geometry in the connectivity matrix induces nested coherent and incoherent regions.

show abstract

Section: Introductionmentioning

confidence: 99%

Robustness of chimera states for coupled FitzHugh-Nagumo oscillators

et al. 2015

View full text Add to dashboard Cite

show abstract

“…To quantify the network synchronization we measured the phase synchronization (PS; Singer, 1999; Varela et al, 2001; Boccaletti et al, 2002; Newman, 2003; Arenas et al, 2008; Baruchi et al, 2008; Filatova et al, 2008; Li et al, 2008; Zanin et al, 2008; Fuchs et al, 2009) between every pair of neurons in the networks. As detailed below, PS is a measure of the coordination (or coherence) between the firing of two neurons – in other words, the expectation that when one neuron fires the second one will fire within a constant phase shift (time delay).…”

Section: Methodsmentioning

confidence: 99%

Reduced Synchronization Persistence in Neural Networks Derived from Atm-Deficient Mice

et al. 2011

Self Cite

View full text Add to dashboard Cite

Many neurodegenerative diseases are characterized by malfunction of the DNA damage response. Therefore, it is important to understand the connection between system level neural network behavior and DNA. Neural networks drawn from genetically engineered animals, interfaced with micro-electrode arrays allowed us to unveil connections between networks’ system level activity properties and such genome instability. We discovered that Atm protein deficiency, which in humans leads to progressive motor impairment, leads to a reduced synchronization persistence compared to wild type synchronization, after chemically imposed DNA damage. Not only do these results suggest a role for DNA stability in neural network activity, they also establish an experimental paradigm for empirically determining the role a gene plays on the behavior of a neural network.

show abstract

“…That means the decrement in the value of α results in restoration of synchronized oscillation from different types of death states even in a large network of coupled oscillators. This synchronized oscillations can be characterized by master stability function [38][39][40].…”

Section: A Landau-stuart Oscillatormentioning

confidence: 99%

Restoration of oscillation in network of oscillators in presence of direct and indirect interactions

Majhi

Bera

Bhowmick³

et al. 2016

Physics Letters A

View full text Add to dashboard Cite

The suppression of oscillations in coupled systems may lead to several unwanted situations, which requires a suitable treatment to overcome the suppression. In this paper, we show that the environmental coupling in the presence of direct interaction, which can suppress oscillation even in a network of identical oscillators, can be modified by introducing a feedback factor in the coupling scheme in order to restore the oscillation. We inspect how the introduction of the feedback factor helps to resurrect oscillation from various kind of death states. We numerically verify the resurrection of oscillations for two paradigmatic limit cycle systems, namely Landau-Stuart and Van der Pol oscillators and also in generic chaotic Lorenz oscillator. We also study the effect of parameter mismatch in the process of restoring oscillation for coupled oscillators.

show abstract

Synchronization in networks of spatially extended systems

Cited by 19 publications

References 48 publications

Robustness of chimera states for coupled FitzHugh-Nagumo oscillators

Robustness of chimera states for coupled FitzHugh-Nagumo oscillators

Reduced Synchronization Persistence in Neural Networks Derived from Atm-Deficient Mice

Restoration of oscillation in network of oscillators in presence of direct and indirect interactions

Contact Info

Product

Resources

About