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When propagated action potentials in cardiac tissue interact with local heterogeneities, reflected waves can sometimes be induced. These reflected waves have been associated with the onset of cardiac arrhythmias, and while their generation is not well understood, their existence is linked to that of one-dimensional (1D) spiral waves. Thus, understanding the existence and stability of 1D spirals plays a crucial role in determining the likelihood of the unwanted reflected pulses. Mathematically, we probe these issues by viewing the 1D spiral as a time-periodic antisymmetric source defect. Through a combination of direct numerical simulation and continuation methods, we investigate existence and stability of a 1D spiral wave in a qualitative ionic model to determine how the systems propensity for reflections are influenced by system parameters. Our results support and extend a previous hypothesis that the 1D spiral is an unstable periodic orbit that emerges through a global rearrangement of heteroclinic orbits and we identify key parameters and physiological processes that promote and deter reflection behavior.
In this paper we present the results of parallel numerical computations of the long-term dynamics of linked vortex filaments in a three-dimensional FitzHugh-Nagumo excitable medium. In particular, we study all torus links with no more than 12 crossin
Recent work has explored binary waveguide arrays in the long-wavelength, near-continuum limit, here we examine the opposite limit, namely the vicinity of the so-called anti-continuum limit. We provide a systematic discussion of states involving one,
A free vortex in excitable media can be displaced and removed by a wave-train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached t
Small-world networks describe many important practical systems among which neural networks consisting of excitable nodes are the most typical ones. In this paper we study self-sustained oscillations of target waves in excitable small-world networks.
A thring is a recent addition to the zoo of spiral wave phenomena found in excitable media and consists of a scroll ring that is threaded by a pair of counter-rotating scroll waves. This arrangement behaves like a particle that swims through the medi