Stimulation of unidirectional pulses in excitable systems

Time-periodic lattice of spiral pairs in excitable media

The feasibility of a spiral-type solution, periodic both in time and in space, of a reaction-diffusion equation (specifically the FitzHugh-Nagumo system) in an excitable medium is numerically demonstrated. The solution consists of arrays of interacting spiral pairs, which repeatedly create by partial annihilation a system of residual portions (RPs). The latter behaves as a source to the next generation of the spiral-pair array. If basic (highest) translational symmetry is not conserved, pointwise perturbations, above a certain threshold, are shown to be able to destroy the pattern after a certain transient time by changing its symmetry. If the basic translational symmetry is preserved, such perturbations do not cause destruction unless occurring at the nearest vicinity of the RP site. Singular value decomposition methods are used to analyze the structure of the pattern, revealing the importance of the spiral pairs and the RPs.

Dynamics of spiral pairs induced by unidirectional propagating pulses

The dynamics of unidirectionally propagating pulses in a two-dimensional uniform excitable reaction-diffusion medium is investigated. It is shown that under weak diffusion coupling between medium points such a pulse can evolve into a pair of counter-rotating spirals (spiral pair). We analyze the drift of such a pair and examine the collisions between several drifting pairs. It is demonstrated that collisions can result in a special type of reflection or, alternatively, in new types of complex stationary spiral structures. A possible application of these findings for the diagnosis of cardiac arrhythmias is suggested.