Synchronization of groups of coupled oscillators with sparse connections

Zheng, Zhigang; Feng, Xun‐Li; Bin, Ao; Cross, M. C.

doi:10.1209/0295-5075/87/50006

Cited by 12 publications

(7 citation statements)

References 19 publications

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“…Notably, small synchronization factors can be tightly associated with states where the formation of spiral waves is robust to mild channel block. A spiral wave is a characteristic spatiotemporal pattern that is often observed in excitable media [1][2][3][4][5][6][7][8][9][10]. The formation and propagation of spiral waves in reaction-diffusion systems have been studied extensively [11][12][13][14][15][16], and some effective schemes have been used to remove spiral waves and prevent ventricular fibrillation [17].…”

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confidence: 99%

Detecting the breakup of spiral waves in small-world networks of neurons due to channel block

Huang

et al. 2012

Chin. Sci. Bull.

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The breakup of a spiral wave by blockade of sodium and potassium channels in a small-world network of Hodgkin-Huxley neurons is investigated in detail. The influence of ion channel block in poisoned excitable membrane patches of a certain size is measured, by varying channel noise and channel densities resulting from the change in conductance. For example, tetraethylammonium is known to cause a block (poisoning) of potassium channels, while tetrodotoxin blocks sodium channels. We observed the occurrence of spiral waves, which are ordered waves believed to play an important role in facilitating the propagation of electric signals across quiescent regions of the brain. In this paper, the effect of channel block was measured by the factors x K and x Na , which represent the ratios of unblocked, or active, ion channels, to the overall number of potassium or sodium ion channels, respectively. To quantify these observations, we use a simple but robust synchronization measure, which succinctly captures the transition from spiral waves to other collective states, such as broken segments resulting from the breakup of the spiral wave. The critical thresholds of channel block can be inferred from the abrupt changes occurring in plots of the synchronization measure against different values of x K and x Na . Notably, small synchronization factors can be tightly associated with states where the formation of spiral waves is robust to mild channel block. A spiral wave is a characteristic spatiotemporal pattern that is often observed in excitable media [1][2][3][4][5][6][7][8][9][10]. The formation and propagation of spiral waves in reaction-diffusion systems have been studied extensively [11][12][13][14][15][16], and some effective schemes have been used to remove spiral waves and prevent ventricular fibrillation [17]. Stable rotating spiral waves have been observed in rat neocortical slices visualized by voltage-sensitive dye imaging [18,19]. Spiral waves might serve as emergent population pacemakers, generating periodic activity in non-oscillatory networks without individual cellular pacemakers. The formation, death, and breakup of spiral waves in the mammalian cortex can be simulated using regular and/or small-world networks [8][9][10].In networks using Hodgkin-Huxley model neurons [20], the effects of channel noise [21,22] on spiral waves needs to be studied in detail.Normal signal propagation between neurons in networks with different topologies deeply depends on the collective behavior of neurons. Abnormalities of neurons in one domain can destroy the normal communication between neurons, and neurological disorders can occur when the normal electrical activity of neurons is violated. The response of neurons to external stimuli (drugs or electrical forcing) is often a result of the collective behaviors of all the neurons in one or more domains. It is reliable to study the collective electrical activities of neurons in functional domains using complex network schemes. Most previous schemes have been proposed to remove spira...

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confidence: 99%

Detecting the breakup of spiral waves in small-world networks of neurons due to channel block

Huang

et al. 2012

Chin. Sci. Bull.

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“…When the coupling strength is strong or the memory of environment is considered, the dynamics of the quantum open systems will be described by a non‐Markovian master equation, which is more general and includes the information flowing from the environment back to the system . Besides the use of the Markovian or non‐Markovian master equation, non‐Hermitian Hamiltonian is another spectacular tool to describe an open system and abundance of efforts have been devoted to it …”

Section: Introductionmentioning

confidence: 99%

Effect of Environment on the Scattering of Electrons by a Junction of Different Topological Materials

Shao

2020

Annalen der Physik

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The studies of electron transport through a junction of topological materials in the literature so far ignore the coupling of a topological material to its surrounding environment. Here, the dynamics of an open system through a stochastic Hamiltonian are simulated to investigate the influence of the environment on the scattering of electrons by a junction of different topological materials, such as a Dirac–Weyl magnetic junction and a topological insulator. It is found that, although the detrimental effect of the environment is inevitable, the Landauer conductance can be enhanced via adjusting the system–environment coupling strength. This result supplies the possibilty of changing the transport feature of topological materials by modulating the surrounded environment. It is also demonstrated that a non‐Hermitian Hamiltonian can be used to replace the stochastic Hamiltonian for this study, when the system and the environment coupling are weak.

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“…[14]. The benefits of synchronization do not lie only in those situations where it can be found or explained in nature, but also in possible technological applications such as communication engineering, biology, chemistry and so on [15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Synchronization enhancement via an oscillatory bath in a network of self-excited cells

2015

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Abstract. The possibility of using a dynamic environment to achieve and optimize phase synchronization in a network of self-excited cells with free-end boundary conditions is addressed in this paper. The dynamic environment is an oscillatory bath coupled linearly to a network of four cells. The boundaries of the stable solutions of the dynamical states as well as the ranges of coupling parameters leading to stability and instability of synchronization are determined. Numerical simulations are used to check the accuracy and to complement the result obtained from analytical treatment. The robustness of synchronization strategy is tested using a local and global injection of Gaussian white noise in the network. The control gain parameter of the bath coupling can modulate the occurrence of synchronization in the network without prior requirement of direct coupling among all the cells. The process of synchronization obtained through local injection is independent of the node at which noise is injected into the system. As compared to local injection, the global injection scheme increases the range of noise amplitude for which synchronization occurs in the network.

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Synchronization of groups of coupled oscillators with sparse connections

Cited by 12 publications

References 19 publications

Detecting the breakup of spiral waves in small-world networks of neurons due to channel block

Detecting the breakup of spiral waves in small-world networks of neurons due to channel block

Effect of Environment on the Scattering of Electrons by a Junction of Different Topological Materials

Synchronization enhancement via an oscillatory bath in a network of self-excited cells

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