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Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions…
Spiral waves in active media react to small perturbations as particle-like objects. Here we apply the asymptotic theory to the interaction of spiral waves with a localized inhomogeneity, which leads to a novel prediction: drift of the…
Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating…
The structure of spiral waves is investigated in super-excitable reaction-diffusion systems where the local dynamics exhibits multi-looped phase space trajectories. It is shown that such systems support stable spiral waves with broken…
Excitable media are systems which are at rest in the absence of external input but which respond to a sufficiently strong stimulus by sending a wave of "excitation" across the medium. Examples include cardiac and cortical tissue, and in…
The dynamics of activation waves in excitable media can give rise to spiral turbulence, the resulting spatiotemporal chaos being associated with empirical biological phenomena such as life-threatening disturbances in the natural rhythm of…
Spiral waves in two-dimensional excitable media have been observed experimentally and studied extensively. It is now well-known that the symmetry properties of the medium of propagation drives many of the dynamics and bifurcations which are…
I present the numerical computation of speed and direction of the drift of a spiral wave in an excitable medium in the presence of an electric field. In contrast to earlier results, the drift speed presents a strong variation close to the…
Spiral wave patterns observed in models of cardiac arrhythmias and chemical oscillations develop alternans and stationary line defects, which can both be thought of as period-doubling instabilities. These instabilities are observed on…
Excitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial dimensions. Examples include waves during a pandemic…
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…
We study a heretofore ignored class of spiral patterns for oscillatory media as characterized by the complex Landau-Ginzburg model. These spirals emerge from modulating the growth rate as a function of $r$, thereby turning off the…
Trapping and un-trapping of spiral tips in a two-dimensional homogeneous excitable medium with local small-world connections is studied by numerical simulation. In a homogeneous medium which can be simulated with a lattice of regular…
Many multicellular communities propagate signals in a directed manner via excitable waves. Cell-to-cell heterogeneity is a ubiquitous feature of multicellular communities, but the effects of heterogeneity on wave propagation are still…
Spatial variations in the electrical properties of cardiac tissue can occur because of cardiac diseases. We introduce such gradients into mathematical models for cardiac tissue and then study, by extensive numerical simulations, their…
Re-entrant spiral waves are observed in many different situations in nature, perhaps most importantly in excitable electrophysiological tissue where they are believed to be responsible for pathological conditions such as cardiac…
Rotating spiral waves organize spatial patterns in chemical, physical and biological excitable systems. Factors affecting their dynamics such as spatiotemporal drift are of great interest for par- ticular applications. Here, we propose a…
Spiral wave propagation in period-2 excitable media is often accompanied by line-defects, the locus of points with period-1 oscillations. Here we investigate spiral line-defects in cardiac tissue where period-2 behavior has a known…
In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral…
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as point-like objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this…