Shape deformation and electromagnetic induction affect wave stability in a memristive media

In this article, a reaction-diffusion model with two variables is improved by incorporating a variable for magnetic flux and a memristive model for excitable media is proposed, in which a magnetic-flux-controlled memristive current is introduced to describe the effect of electromagnetic induction. The memristive excitable model can induce different wave fronts for developing ordered waves, and the effect of shape deformation in the media is quantified under constant size of the media. The deformation effect is in line with the area-preserving transformation. In fact, the deformation effect can be equivalently represented as the coupling strength in the horizontal and vertical directions, as a result, the diffusion coefficients along horizontal and vertical direction in the media become complementary when shape deformation occurs. For example, DxDy = D'xD'y, where Dx and Dy represent diffusion coefficient without shape deformation, D'x and D'y denote new diffusion coefficients after shape deformation in the media. The three-variable memristive model is updated with an equivalent network after discretization, and the coupling intensity between adjacent nodes along horizontal and vertical directions compensate with each other. Wave propagation and pattern formation in this network are discussed, and numerical results show that deformation amplitude and memristive strength jointly regulate spiral wave stability and synchronization degree, which is measured by the synchronization factor. For anisotropic media, shape deformation in the media seldom supports complementary changes in the diffusion coefficients along two different directions and wave breakup occurs. It is found that strong deformation or weak electromagnetic feedback tends to destabilize ordered waves, whereas appropriate memristive parameter B can enhance global synchronization and suppress spiral breakup. The presented results provide possible help for estimating the stability of wave propagation in cardiac tissue.