Control of turbulence in heterogeneous excitable media

Lou, Qin; Chen, Jiang-Xing; Zhao, Yue; Shen, Farong; Fu, Yiming; Wang, Lulu; Liu, Yan

doi:10.1103/physreve.85.026213

Cited by 27 publications

(13 citation statements)

References 41 publications

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“…(5)- (7). When r>r c , the arms in multi-armed dense spirals will rotate independently just like 1-armed dense spiral.…”

Section: Conclusion and Remarksmentioning

confidence: 99%

Interaction of multiarmed spirals in bistable media

Liu

2013

Phys. Rev. E

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We study the interaction of both dense and sparse multi-armed spirals in bistable media modeled by equations of FitzHugh-Nagumo type. Dense 1-armed spiral is characterized by its fixed tip. For dense multi-armed spirals, when the initial distance between tips is less than a critical value, the arms collide, connect and disconnect continuously as the spirals rotate. The continuous reconstruction between the front and the back drives the tips to corotate along a rough circle and to meander zigzaggedly. The rotation frequency of tip, the frequency of zigzagged displacement, the frequency of spiral, the oscillation frequency of media, and the number of arms satisfy certain relations as long as the control parameters of the model are fixed. When the initial distance between tips is larger than the critical value, the behaviors of individual arms within either dense or sparse multi-armed spirals are identical to that of corresponding 1-armed spirals.

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“…(5)- (7). When r>r c , the arms in multi-armed dense spirals will rotate independently just like 1-armed dense spiral.…”

Section: Conclusion and Remarksmentioning

confidence: 99%

Interaction of multiarmed spirals in bistable media

Liu

2013

Phys. Rev. E

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“…It was confirmed that optimized noise on network can be active to develop a spiral wave [40] due to coherence resonance [41] , [42] . More often, target wave can also be induced in the media due to heterogeneity [43] and the emitting wave can be used to suppress the spiral wave and turbulence of the media [44] , for example, the tip dynamics of spiral wave is changed by the fractal heterogeneity [43] , and the heterogeneity by a rotating electric field [45] can emit ordered wave to regulate the behavior of excitable media.…”

Section: Introductionmentioning

confidence: 99%

Autapse-Induced Spiral Wave in Network of Neurons under Noise

Qin

Wang

et al. 2014

PLoS ONE

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Autapse plays an important role in regulating the electric activity of neuron by feedbacking time-delayed current on the membrane of neuron. Autapses are considered in a local area of regular network of neurons to investigate the development of spatiotemporal pattern, and emergence of spiral wave is observed while it fails to grow up and occupy the network completely. It is found that spiral wave can be induced to occupy more area in the network under optimized noise on the network with periodical or no-flux boundary condition being used. The developed spiral wave with self-sustained property can regulate the collective behaviors of neurons as a pacemaker. To detect the collective behaviors, a statistical factor of synchronization is calculated to investigate the emergence of ordered state in the network. The network keeps ordered state when self-sustained spiral wave is formed under noise and autapse in local area of network, and it independent of the selection of periodical or no-flux boundary condition. The developed stable spiral wave could be helpful for memory due to the distinct self-sustained property.

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“…The dynamics of a spiral wave in a reaction-diffusion system has been investigated extensively, and it is confirmed that the formation of a spiral wave in cardiac tissue could be associated with specific types of arrhythmias (reentrant ventricular tachycardia and ventricular fibrillation) [26], [27]. Some reliable theoretical models [28]–[31] have been proposed to measure the dynamics of spiral waves, and some feasible schemes [32]–[36] have been presented to suppress the spiral wave turbulence, and to prevent the breakup [37] of spiral waves. Spiral waves and target waves [38]–[41] are ordered waves, and these waves are often observed in the excitable media.…”

Section: Introductionmentioning

confidence: 93%

The Formation Mechanism of Defects, Spiral Wave in the Network of Neurons

2013

PLoS ONE

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A regular network of neurons is constructed by using the Morris-Lecar (ML) neuron with the ion channels being considered, and the potential mechnism of the formation of a spiral wave is investigated in detail. Several spiral waves are initiated by blocking the target wave with artificial defects and/or partial blocking (poisoning) in ion channels. Furthermore, possible conditions for spiral wave formation and the effect of partial channel blocking are discussed completely. Our results are summarized as follows. 1) The emergence of a target wave depends on the transmembrane currents with diversity, which mapped from the external forcing current and this kind of diversity is associated with spatial heterogeneity in the media. 2) Distinct spiral wave could be induced to occupy the network when the target wave is broken by partially blocking the ion channels of a fraction of neurons (local poisoned area), and these generated spiral waves are similar with the spiral waves induced by artificial defects. It is confirmed that partial channel blocking of some neurons in the network could play a similar role in breaking a target wave as do artificial defects; 3) Channel noise and additive Gaussian white noise are also considered, and it is confirmed that spiral waves are also induced in the network in the presence of noise. According to the results mentioned above, we conclude that appropriate poisoning in ion channels of neurons in the network acts as ‘defects’ on the evolution of the spatiotemporal pattern, and accounts for the emergence of a spiral wave in the network of neurons. These results could be helpful to understand the potential cause of the formation and development of spiral waves in the cortex of a neuronal system.

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Control of turbulence in heterogeneous excitable media

Cited by 27 publications

References 41 publications

Interaction of multiarmed spirals in bistable media

Interaction of multiarmed spirals in bistable media

Autapse-Induced Spiral Wave in Network of Neurons under Noise

The Formation Mechanism of Defects, Spiral Wave in the Network of Neurons

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