Antispirals in an artificial tissue of oscillatory cells

Skødt, Henrik; Sørensen, Preben Graae

doi:10.1103/physreve.68.020902

Cited by 16 publications

(12 citation statements)

References 17 publications

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“…The inwardly propagating spirals (IPSs) were first observed in the oscillatory BZ reaction dispersed in water droplets of a water-in-oil microemulsion [15]. Since then, they have also been discovered in some other systems, such as the single-phase reaction-diffusion (RD) system [16], the artificial tissue of oscillatory cells [17], oscillatory glycolysis [18], etc., and have been extensively studied (see, e.g., Refs. [19][20][21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

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: 99%

Chiralities of spiral waves and their transitions

Pan

Cai

et al. 2013

Phys. Rev. E

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“…[12,13,14,15,16,17,18]. More recent reports have adapted the new name antispiral in the sense it is used here [19,20]. The distinction achieved here by the prefix anti is sometimes also referred to as positive dispersion (spiral) and negative dispersion (antispiral) [18].…”

Section: Introductionmentioning

confidence: 99%

Antispiral Waves as Sources in Oscillatory Reaction−Diffusion Media

2004

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Spiral and antispiral waves are studied numerically in two examples of oscillatory reaction-diffusion media and analytically in the corresponding complex Ginzburg-Landau equation (CGLE). We argue that both these structures are sources of waves in oscillatory media, which are distinguished only by the sign of the phase velocity of the emitted waves. Using known analytical results in the CGLE, we obtain a criterion for the CGLE coefficients that predicts whether antispirals or spirals will occur in the corresponding reaction-diffusion systems. We apply this criterion to the FitzHugh-Nagumo and Brusselator models by deriving the CGLE near the Hopf bifurcations of the respective equations. Numerical simulations of the full reaction-diffusion equations confirm the validity of our simple criterion near the onset of oscillations. They also reveal that antispirals often occur near the onset and turn into spirals further away from it. The transition from antispirals to spirals is characterized by a divergence in the wavelength. A tentative interpretaion of recent experimental observations of antispiral waves in the Belousov-Zhabotinsky reaction in a microemulsion is given.

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“…The recent discovery of antispiral and antitarget waves in reaction-diffusion systems [1][2][3] has attracted much interest because of a unique characteristic: the wave's phase velocity is opposite to their group velocity [4,5]. A normal concentric or spiral wave in a reaction-diffusion system has outward propagation from its wave source, because its phase velocity and group velocity point to the same direction.…”

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confidence: 99%