Related papers: Computation of the response functions of spiral wa…
Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. In the presence of a small perturbation, the spiral wave's centre of rotation and fiducial phase may…
Dynamics of spiral waves in perturbed, e. g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of…
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…
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a…
This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred…
Rotating spiral waves with a central core composed of phase-randomized oscillators can arise in reaction-diffusion systems if some of the chemical components involved are diffusion-free. This peculiar phenomenon is demonstrated for a…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
In two-dimensional reaction-diffusion systems, local curvature perturbations in the shape of traveling waves are typically damped out and disappear in the course of time. If, however, the inhibitor diffuses much faster than the activator,…
We discovered a new type of spiral wave solutions in reaction-diffusion systems --- spike spiral wave, which significantly differs from spiral waves observed in FitzHugh-Nagumo-type models. We present an asymptotic theory of these waves in…
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…
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…
Rotors of reaction and diffusion, that revolve around a circular singularity, and the corresponding spiral wave activity around it, influence the nature of several excitable media. Their dynamics are known to be affected by target waves and…
A computational linear stability analysis of spiral waves in a reaction-diffusion equation is performed on large disks. As the disk radius R increases, eigenvalue spectra converge to the absolute spectrum predicted by Sandstede and Scheel.…
Rotating spiral waves without phase singularity are found to arise in a certain class of three-component reaction-diffusion systems of biological relevance. It is argued that this phenomenon is universal when some chemical components…
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 waves emerge in numerous pattern forming systems and are commonly modeled with reaction-diffusion systems. Some systems used to model biological processes, such as ion-channel models, fall under the reaction-diffusion category and…
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 and antispiral waves are studied numerically in two examples of oscillatory reaction-diffusion media and analytically in the corresponding complex Ginzburg-Landau equation (CGLE). We argue that both these structures are sources of…
We study the drift of spiral waves in a simple model of heterogeneous excitable medium, having gradients in local excitability or cellular coupling. For the first time, we report the anomalous drift of spiral waves towards regions having…
Interacting rotating spiral waves have been observed in complex systems, such as cardiac fibrillation, cognitive processing in the brain cortex and oscillating chemical reactions, during dynamical regimes that are still poorly understood.…