Spatio-temporal patterns in two-dimensional excitable media subject to Robin boundary conditions

摘要

A numerical study of spiral wave propagation in two-dimensional excitable media subject to homogeneous Robin boundary conditions is presented, and it is shown that, depending on the magnitude of the transfer coefficient, periodic, almost periodic and nonperiodic dynamics may be observed. For transfer coefficients equal to or smaller than one, spiral waves almost identical to those obtained with homogeneous Neumann boundary conditions are observed, whereas arms of spiral waves, layers along the boundaries of the domain, break-up, attachment to and detachment from boundaries, islands and complex spatio-temporal patterns result when the transfer coefficients for both the activator and inhibitor are larger than one along either the top and bottom boundaries or the left and right boundaries. When the transfer coefficients are larger than one along all the boundaries of the domain, it has been found that there is a layer of high activator’s concentration along the boundaries and an arm of spiral waves may appear and interact with the boundary layers, and the dynamics of the excitable medium is complex and nonperiodic.