Generation of finite wave trains in excitable media

Abstract

Spatiotemporal control of excitable media is of paramount importance in the development of new applications, ranging from biology to physics. To this end, we identify and describe a qualitative property of excitable media that enables us to generate a sequence of traveling pulses of any desired length, using a one-time initial stimulus. The wave trains are produced by a transient pacemaker generated by a one-time suitably tailored spatially localized finite amplitude stimulus, and belong to a family of fast pulse trains. A second family, of slow pulse trains, is also present. The latter are created through a clumping instability of a traveling wave state (in an excitable regime) and are inaccessible to single localized stimuli of the type we use. The results indicate that the presence of a large multiplicity of stable, accessible, multi-pulse states is a general property of simple models of excitable media.

Nonlinear and stochastic dynamics in the heart

“…Focal excitations can also occur in homogeneous tissue via pattern formation. In a study by Yochelis et al [490], localized pacemaker sites can form in a homogeneous excitable medium via an instability similar to the Turing instability, in which the inhibitor diffuses much faster than the activator. However, this condition is not feasible in cardiac tissue in which only voltage diffuses.…”

Anomalous dispersion in the Belousov–Zhabotinsky reaction: Experiments and modeling

“…Experimentally dispersion relations with a single overshoot were found in the catalytic reduction of NO with CO on platinum surfaces [10], a BZ-type reaction in which malonic acid is replaced by 1,4-cyclohexanedione (CHD) [11,12], and possibly the slime mold Dictyostelium discoideum [13]. We would also like to mention some recent publications on the attractive interaction between pulses [14] and on the interaction of pulses with pacemakers [15]. This Article discusses three distinct types of wave dynamics in the CHD-BZ reaction and analyzes a reaction-diffusion model that qualitatively reproduces these phenomena.…”

Spatial localization in heterogeneous systems

“…In addition, localized bump forcing may serve as a model of a persistent perturbation, such as may be applied by a focused optical probe in an optics experiment, in contrast to instantaneous perturbations applied by turning the probe rapidly on and off. The latter example leads to initial value evolution with a different initial condition; the former can lead to persistent structures trapped by the inhomogeneity whose properties may be tailored by appropriate shaping of the bump profile [45].…”