Antispiral waves in reaction-diffusion systems
We report spontaneous antispiral wave formation in typical reaction-diffusion systems: the complex Ginzburg-Landau equation, the FitzHugh-Nagumo model, and the Oregonator model of the Belousov-Zhabotinsky chemical reaction. Our findings qualitatively reproduce a series of phenomena, including antispiral waves, accelerating waves, and small amplitude oscillating (packet) waves, recently observed in a Belousov-Zhabotinsky-type chemical reaction. In these models, antispiral waves can only occur near the Hopf bifurcation, when the system is characterized by small amplitude oscillatory (as opposed to excitable) dynamics. For reaction-diffusion systems in the vicinity of the Hopf bifurcation, the condition required for antispiral formation is established through both theoretical analyses of the complex Ginzburg-Landau equation and numerical simulations of the FitzHugh-Nagumo model and the Oregonator model of the Belousov-Zhabotinsky chemical reaction. For more information, please see "Antispiral waves in reaction-diffusion systems," [Physical Review Letters, 90, article 088302 (2003)].
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This movie shows the birth sequence of antispiral waves in the CGL equation intitiating from random initial conditions. Click on the image to download and view the movie (1919 kB).
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This movie shows antispiral waves in the complex Ginzburg-Landau equation, which is the prototype of an oscillatory medium close to the Hopf bifurcation point. Click on the image to download and view the movie (955 kB).
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This movie shows antispiral waves in the FHN model. Note the inward propagation of the white wavefront. Click on the image to download and view the movie (1275 kB).
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This movie shows antispiral waves in the Oregonator model of the Belousov-Zhabotinsky chemical reaction. Note the inward propagation of the white wavefront. Click on the image to download and view the movie (958 kB).
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