Introduction
The ''reverberator'' was one of the first autowave solutions, researchers found, and, because of this historical context, it remains by nowadays the most studied autowave object. Up until the late 20th century, the term "''auto-wave reverberator''" was used very active and widely in the scientific literature, written by soviet authors, because of active developing these investigations inBasic information
"Historical" definition
On the question of terminology
Types of reverberator behaviour
The "classical" regimes
Various autowave regimes, such as ''plane waves'' or ''spiral waves'' can exist in an active media, but only under certain conditions on the medium properties. Using the FitzhHugh-Nagumo model for a generic active medium, Winfree constructed a diagram depicting the regions of parameter space in which the principle phenomena may be observed. Such diagrams are a common way of presenting the different dynamical regimes observed in both experimental and theoretical settings. They are sometimes called ''flower gardens'' since the paths traced by autowave tips may often resemble the petals of a flower. A flower garden for the FitzHugh-Nagumo model is shown to the right. It contains: the line ''∂P'', which confines the range of the model parameters under which impulses can propagate through one-dimensional medium, and ''plane autowaves'' can spread in the two-dimensional medium; the "rotor boundary" ''∂R'', which confines the range of the parameters under which there can be the reverberators rotating around fixed cores (i.e. performing uniform circular rotation); the ''meander'' boundary ''∂M'' and the ''hyper-meander'' boundary ''∂C'', which confine the areas where two-period and more complex (possibly chaotic) regimes can exist. Rotating autowaves with large cores exist only in the areas with parameters close to the boundary ''∂R''. Similar autowave regimes were also obtained for the other models — Beeler-Reuter model, Barkley model, Aliev-Panfilov model, Fenton-Karma model etc. It was also shown that these simple autowave regimes should be common to all active media because a system ofRegimes of induced drift
At meander and hyper-meander, the displacement of the center of autowave rotation (i.e. its drift) is influenced by the forces generated by the very same rotating autowave. However, in result of the scientific study of rotating autowaves was also identified a number of external conditions that force reverberator drift. It can be, for example, the heterogeneity of the active medium by any parameter. Perhaps, it is the works Biktasheva, where different types of the reverberator drift are currently represented the most completely (although there are other authors who are also involved in the study of drift of the autowave reverberator). In particular, Biktashev offers to distinguish the following types of reverberator drift in the active medium: # Resonant drift. # Inhomogeneity induced drift. # Anisotropy induced drift. # Boundary induced drift (see also). # Interaction of spirals. # High frequency induced drift. Note that even for such a simple question, what should be called a drift of autowaves, and what should not be called, there is still no agreement among researchers. Some researchers (mostly mathematicians) tends to consider as reverberator drift only those of its displacement, which occur under the influence of external events (and this view is determined exactly by the peculiarity of the mathematical approach to the study of autowaves). The other part of the researchers did not find significant differences between the spontaneous displacement of reverberator in result of the events generated by it itself, and its displacement as a result of external influences; and therefore these researchers tend to believe that meander and hyper-meander are also variants of drift, namely ''the spontaneous drift of the reverberator''. There was not debate on this question of terminology in the scientific literature, but it can be found easily these features of describing the same phenomena by the different authors.Autowave lacet
In the numerical study of reverberator using the Aliev-Panfilov model, the phenomenon ofThe reasons for distinguishing between variants of rotating autowaves
Recall that from 1970th to the present time it is customary to distinguish three variants rotating autowaves: # wave in the ring, # spiral wave, # autowave reverberator. Dimensions of the core of reverberator is usually less than the minimal critical size of the circular path of circulation, which is associated with the phenomenon of ''critical curvature''. In addition, the refractory period appears to be longer for the waves with non-zero curvature (reverberator and spiral wave) and begins to increase with decreasing the excitability of the medium before the refractory period for the plane waves (in the case of circular rotation). These and other significant differences between the reverberator and the circular rotation of excitation wave make us distinguish these two regimes of re-entry. The figure shows the differences found in the behavior of the plane autowave circulating in the ring and reverberator. You can see that, in the same local characteristics of the excitable medium (excitability, refractoriness, etc., given by the nonlinear member), there are significant quantitative differences between dependencies of the reverberator characteristics and characteristics of the regime of one-dimensional rotation of impulse, although respective dependencies match qualitatively.Notes
References
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