Ordered waves in a memristive excitable media under asymmetrical diffusion

An external electric field can induce polarization effects in the excitable media and the inner diffusion of intracellular ions is modified, accompanying by appropriate shape deformation in the media. Polarization effect supports orderliness when the medium suffers from external applied electric field, and appropriate shape deformation is induced in the flexible media, including cardiac tissue and some chemical reactions. In this article, we extend an excitable medium model by incorporating both memristive electromagnetic induction and shape deformation, and further establish an equivalent network framework to investigate the resulting collective dynamics. In one-layer excitable media, the media size (L _x ·L _y ) maintains a constant, and shape deformation seldom changes the media size, as a result, the two diffusion coefficients (D _x , D _y ) become complementary with time. The local kinetics of the memristive media is discussed, and the reaction-diffusion equations are converted into equivalent coupled neural network for exploring collective behaviors, including wave propagation and synchronization stability. The shape deformation induces changes of the diffusion coefficients in opposite way, with one direction enhanced and the other weakened, and the wave stability is modified because asymmetrical diffusion in the media. Incorporation of the memristive current and shape deformation into the excitable can better reflect the physical effect in the excitable media well.