Abstract
Spiral waves are shown to undergo directional drifts in the presence of ac and polarized electric fields when their frequencies are twice of the spiral frequencies. Here, we propose a quantitative description for the spiral wave drift induced by weak electric fields, and provide the explicit equations for the spiral wave drift speed and direction. Numerical simulations are performed to demonstrate the quantitative agreement with analytical results in both weakly and highly excitable media.
Highlights
Excitable media represent a wide class of nonequilibrium systems which play an important role in physical, chemical, and biological applications[1, 2]
The authors in ref. 14 reported the first experimental observation of a directional drift of the spiral wave along a straight line, during the periodic modulation of the excitability of an excitable medium with a frequency close to the nature rotation frequency of the spiral. This directional drift phenomenon for spiral waves subjected to the external periodic forcing has been confirmed in numerous experiments as well as numerical simulations
The mechanism of the directional drift of spiral waves subjected to the external periodic forcing was studied and a drift velocity formula for spirals was obtained
Summary
A drift velocity formula in terms of the electric fields, the response functions, the Goldstone modes, and the initial rotation phase of the spiral is given. Opposite rotation between the spiral and electric field (φxy = 1.5π) locks the spiral Explicit equations for the spiral wave drift speed and direction in terms of Φ, E0, φe, and φxy are obtained directly from the reaction diffusion equations, which are independent of the special models and should be of general significance These analytical results are quantitatively confirmed by numerical simulations in both weakly and highly excitable media. We hope that the theoretical results in Eqs (11) and (13) can be verified in experiments
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