Chimera states in bursting neurons

Bera, Bidesh K.; Ghosh, Dibakar; Lakshmanan, M.

doi:10.1103/physreve.93.012205

Cited by 172 publications

(103 citation statements)

References 60 publications

Supporting

Mentioning

101

Contrasting

Unclassified

Order By: Relevance

“…In particular, Hindmarsh-Rose neural oscillators have been studied in networks with nonlocal [15] and nearestneighbor [16] coupling, as well as in modular networks consisting of communities [17]. Potential relevance of chimera states in this context include bump states [18,19] and the phenomenon of unihemispheric sleep observed in birds and dolphins [20], which sleep with one eye open, meaning that half of the brain is synchronous with the other half being asynchronous.…”

Section: Introductionmentioning

confidence: 99%

Chimera patterns in two-dimensional networks of coupled neurons

et al. 2017

View full text Add to dashboard Cite

We discuss synchronization patterns in networks of FitzHugh-Nagumo and Leaky Integrate-andFire oscillators coupled in a two-dimensional toroidal geometry. Common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes including spots, rings, stripes, and grids, observed in both models, as well as additional patterns found mainly in the FitzHughNagumo system. Both systems exhibit multistability: For the same parameter values, different initial conditions give rise to different dynamical states. Transitions occur between various patterns when the parameters (coupling range, coupling strength, refractory period, and coupling phase) are varied. Many patterns observe in the two models follow similar rules. For example the diameter of the rings grows linearly with the coupling radius.

show abstract

Section: Introductionmentioning

confidence: 99%

Chimera patterns in two-dimensional networks of coupled neurons

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Химерные состояния были обнаружены в сетях с различной топологией связей. В частности, в работе [6] на примере сети нейронов Хиндмарш-Роуз химерные состояния были получены для случаев глобальной, нелокальной и даже локальной связи. Помимо симметричных связей, в работе [7] также была продемонстрирована возможность реализации химерных состояний в свободно масштабируемой (англ.…”

unclassified

Взаимодействие Химерных Состояний В Многослойной Сети Нелокально Связанных Осцилляторов

Горемыко¹,

Максименко²,

Макаров³

et al. 2017

Письма В Журнал Технической Физики

View full text Add to dashboard Cite

Изучены процессы возникновения и эволюции химерных состояний в модели многослойной сети нелинейных элементов со сложной топологией связей. В качестве объекта исследования рассмотрена двухслойная сеть нелокально связанных в пределах слоя фазовых осцилляторов Курамото-Сакагучи. Про-демонстрированы различные режимы, реализующиеся в данной системе при изменении степени взаимодействия между слоями сети.

show abstract

“…It has been mimicked in laboratory experiments [18][19][20][21] too. Some recent reports have also identified chimera states in neuronal systems 5,7,22,23 and superconducting Josephson junctions 24,25 , which encourage a search for future application possibilities. Recent studies have also reported emergence of chimera states in multiplex networks 26 .…”

Section: Introductionmentioning

confidence: 99%

“…Besides synchronization and clustering in a network of oscillators, the emergence of chimera states in identical oscillators under nonlocal coupling 1-3 and, even for global coupling 4 and nearest neighbor coupling [5][6][7][8] have received significant attention in recent years. The chimera states emerge as a surprising symmetry breaking in a homogeneous population of identical oscillators into two coexisting synchronous and asynchronous subpopulations; the mechanism of such a symmetry breaking is yet to be unraveled completely.…”

Section: Introductionmentioning

confidence: 99%

“…We adopt a simpler approach, atypical of the conventional approaches [1][2][3][4][5][6][7][8]32 , but the traditional self-feedback technique to create and control chimera-like coexisting coherent and incoherent subpopulations in an open chain of identical oscillators. The size of the coherent and the incoherent subpopulations is an emergent property and usually undetermined, however, we find that it is controllable by the feedback control mechanism.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control

Bera

Ghosh

Parmananda

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

View full text Add to dashboard Cite

We report the emergence of coexisting synchronous and asynchronous subpopulations of oscillators in one dimensional arrays of identical oscillators by applying a self-feedback control. When a self-feedback is applied to a subpopulation of the array, similar to chimera states, it splits into two/more sub-subpopulations coexisting in coherent and incoherent states for a range of self-feedback strength. By tuning the coupling between the nearest neighbors and the amount of self-feedback in the perturbed subpopulation, the size of the coherent and the incoherent sub-subpopulations in the array can be controlled, although the exact size of them is unpredictable. We present numerical evidence using the Landau-Stuart (LS) system and the KuramotoSakaguchi (KS) phase model. The symmetry breaking of a coherent population of identical oscillators under non-local, local and global coupling, into coexisting coherent and incoherent subpopulations is a strange behavior that has been discussed in recent literature of collective behavior of many dynamical systems. Such a self-organized behavior of a homogeneous population of oscillators is called chimera states. We observe emergence of a similar type of splitting into subsets of coexisting synchronous and asynchronous oscillators, when we apply a self-feedback to a coherent subset of oscillators in a locally coupled open chain of identical oscillators. Interestingly, the unperturbed subpopulation remains coherent for higher values of feedback strength. Most encouragingly, it shows a direction how the size of the coherent and the incoherent subpopulations in the chimera pattern can be monitored by playing with the feedback strength. We provide numerical evidence in two such arrays using the Landau-Stuart (LS) system and the Kuramoto-Sakaguchi (KS) phase model.

show abstract

Chimera states in bursting neurons

Cited by 172 publications

References 60 publications

Chimera patterns in two-dimensional networks of coupled neurons

Chimera patterns in two-dimensional networks of coupled neurons

Взаимодействие Химерных Состояний В Многослойной Сети Нелокально Связанных Осцилляторов

Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control

Contact Info

Product

Resources

About