Inwardly rotating spirals in nonuniform excitable media

Gao, Xiang; Feng, Xi‐Qiao; Cai, Mei-Chun; Li, Bingwei; Huang, Ying; Zhang, Hong

doi:10.1103/physreve.85.016213

Cited by 10 publications

(3 citation statements)

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“…[19][20][21][22][23]). In particular, they have also been observed numerically in nonuniform excitable media recently [24]. Now, the relationship between the rotation and the curl directions and the one between the chiralities and the topological charges, which work well for OPSs in uniform excitable media, are not preserved any more.…”

Section: Introductionmentioning

confidence: 97%

Chiralities of spiral waves and their transitions

Pan

Cai

et al. 2013

Phys. Rev. E

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The chiralities of spiral waves usually refer to their rotation directions (the turning orientations of the spiral temporal movements as time elapses) and their curl directions (the winding orientations of the spiral spatial geometrical structures themselves). Traditionally, they are the same as each other. Namely, they are both clockwise or both counterclockwise. Moreover, the chiralities are determined by the topological charges of spiral waves, and thus they are conserved quantities. After the inwardly propagating spirals were experimentally observed, the relationship between the chiralities and the one between the chiralities and the topological charges are no longer preserved. The chiralities thus become more complex than ever before. As a result, there is now a desire to further study them. In this paper, the chiralities and their transition properties for all kinds of spiral waves are systemically studied in the framework of the complex Ginzburg-Landau equation, and the general relationships both between the chiralities and between the chiralities and the topological charges are obtained. The investigation of some other models, such as the FitzHugh-Nagumo model, the nonuniform Oregonator model, the modified standard model, etc., is also discussed for comparison.

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Section: Introductionmentioning

confidence: 97%

Chiralities of spiral waves and their transitions

Pan

Cai

et al. 2013

Phys. Rev. E

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“…He et al [23] detected the transition between Turing pattern and the antispiral waves when time-delay feedback was imposed on the system. Beside from the topic about spiral wave, Gao et al [24] investigated the dynamics of inwardly rotating spiral wave in nonuniform excitable media. Furthermore, Gan et al [25] studied the breakup of spiral wave induced by colored noise.…”

Section: Introductionmentioning

confidence: 99%

Robustness, Death of Spiral Wave in the Network of Neurons under Partial Ion Channel Block

Ma¹,

Long²,

Zhang³

2013

Commun. Theor. Phys.

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The development of spiral wave in a two-dimensional square array due to partial ion channel block (Potassium, Sodium) is investigated, the dynamics of the node is described by Hodgkin-Huxley neuron and these neurons are coupled with nearest neighbor connection. The parameter ratio x Na (and x K ), which defines the ratio of working ion channel number of sodium (potassium) to the total ion channel number of sodium (and potassium), is used to measure the shift conductance induced by channel block. The distribution of statistical variable R in the two-parameter phase space (parameter ratio vs. poisoning area) is extensively calculated to mark the parameter region for transition of spiral wave induced by partial ion channel block, the area with smaller factors of synchronization R is associated the parameter region that spiral wave keeps alive and robust to the channel poisoning. Spiral wave keeps alive when the poisoned area (potassium or sodium) and degree of intoxication are small, distinct transition (death, several spiral waves coexist or multi-arm spiral wave emergence) occurs under moderate ratio x Na (and x K ) when the size of blocked area exceeds certain thresholds. Breakup of spiral wave occurs and multi-arm of spiral waves are observed when the channel noise is considered.

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“…While a study of wave dynamics in homogeneous media is a necessary starting point for clarifying the corresponding theoretical backgrounds, wave processes in inhomogeneous media have always been considered as a fundamental problem for many applications and attract growing interest nowadays. Indeed, it is extremely important to elucidate the role of an inhomogeneity as a factor which affects wave structures existing in homogeneous media or even creates quite unusual ones [11][12][13][14][15][16]. Of course, this is very important for diverse applications because inhomogeneity is quite natural in all real systems.…”

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confidence: 99%

Stationary propagation of a wave segment along an inhomogeneous excitable stripe

et al. 2014

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We report a numerical and theoretical study of an excitation wave propagating along an inhomogeneous stripe of an excitable medium. The stripe inhomogeneity is due to a jump of the propagation velocity in the direction transverse to the wave motion. Stationary propagating wave segments of rather complicated curved shapes are observed. We demonstrate that the stationary segment shape strongly depends on the initial conditions which are used to initiate the excitation wave. In a certain parameter range, the wave propagation is blocked at the inhomogeneity boundary, although the wave propagation is supported everywhere within the stripe. A free-boundary approach is applied to describe these phenomena which are important for a wide variety of applications from cardiology to information processing.

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Inwardly rotating spirals in nonuniform excitable media

Cited by 10 publications

References 50 publications

Chiralities of spiral waves and their transitions

Chiralities of spiral waves and their transitions

Robustness, Death of Spiral Wave in the Network of Neurons under Partial Ion Channel Block

Stationary propagation of a wave segment along an inhomogeneous excitable stripe

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