Antispiral Waves in Reaction-Diffusion Systems

Gong, Yanyun; Christini, David J.

doi:10.1103/physrevlett.90.088302

Cited by 103 publications

(55 citation statements)

References 20 publications

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“…Gong and Christini have recently investigated the CGLE and prototypical two-component reactiondiffusion (RD) models and conjectured that antispirals only occur near the onset of oscillations [24]. We will provide further evidence for their claim.…”

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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Section: Introductionmentioning

confidence: 99%

Antispiral Waves as Sources in Oscillatory Reaction−Diffusion Media

2004

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“…The case σ = −1 refers to so-called anti-spirals [64][65][66], which can appear in oscillatory reactiondiffusion systems. To include anti-spirals into the scope of our approach, Eq.…”

Section: Feedback-mediated Drift Of Spiral Waves In the Ginzburg-landmentioning

confidence: 99%

Feedback-mediated control of spiral waves

Zykov

Engel

2004

Physica D: Nonlinear Phenomena

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“…Previously found waves are generally outgoing, i.e., propagating away from the wave source, till recent observation of waves that propagate toward the source, called ingoing waves (also referred to "antiwaves", e.g., antitarget waves and antispiral waves) in experiments [23,24] as well as in numerical simulations [25][26][27]. In terms of physical language, the outgoing (ingoing) waves have positive (negative) phase velocity.…”

Section: Introductionmentioning

confidence: 98%