Eliminate spiral wave in excitable media by using a new feasible scheme

Abstract

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 ∝ r 2 dB / dt and r = ( 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 ∝ 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 ∝ 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.