Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 15, Issue 7, Pages 1768-1776Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2009.07.013
Keywords
Spiral wave; Fithhugh-Nagumo model; Vortex electric field
Categories
Funding
- National Natural Science Foundation of China [10747005, 10875049]
- Key Project of Chinese Ministry of Education [108096]
- Natural Science of Lanzhou University of Technology [Q200706]
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In this paper, a new scheme is proposed to remove the spiral wave in a two-dimensional Fithhugh-Nagumo type equation by introducing a class of vortex electric field into the media. A long electric solenoid with large pipe diameter is used to generate a spatial magnetic field and the intensity of magnetic field B is controllable. A vortex electric field could be induced by changing the external magnetic field B. The media is polarized and the membrane potential is changed as the vortex electric field is imposed on the media. The polarization effect of the external field on the media is discussed. It argued that the effect of the external electric field could be reproduced with a spatial stimulation current (transformed membrane current)imposed on the media, which is approached by I-ex proportional to r(2)dB/dt and r = root(x - x(0))(2) + (y - y(0))(2), x(0), y(0) is the coordinate origin, (x, y) defines the site position. The spatial polarized field introduces vortex electric current I-ex proportional to r(2)dB/dt into the media and it differs from the external forcing by placing electrode into the media. The external current is transformed into membrane current I-st proportional to r(4)(dB/dt)(2) to change the potential of the membrane. The numerical results confirm that the spiral wave could be removed with appropriate vortex electric field or current. The final state will be stable when the transformed membrane current or the extern polarized field is a constant signal, and the whole system will oscillate periodically when the external polarized field or transformed membrane current is changed with a periodical signal. Furthermore, the spiral wave still be removed even if the spatiotemporal noise is introduced into all the media. (c) 2009 Elsevier B.V. All rights reserved.
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