Autowave

Autowaves are self-supporting non-linear waves in active media (i.e. those that provide distributed energy sources).

The term is generally used in processes where the waves carry relatively low energy, which is necessary for synchronization or switching the active medium.

Belousov became winners of the highest state award of the USSR, Lenin Prize "for the discovery of a new class of autowave processes and the study of them in disturbance of stability of the distributed excitable systems."

The classical axiomatic model with autowaves in myocardium was published in 1946 by Norbert Wiener and Arturo Rosenblueth.

[A: 5] During 1970-80, major efforts to study autowaves were concentrated in the Institute of Biological Physics of the USSR Academy of Sciences, located in the suburban town Pushchino, near Moscow.

Moskalenko gained their experience with the autowave theory also in Pushchino, in the neighboring Institute of Mathematical Problems of Biology, under the guidance of E.E.Shnoll.

Almost immediately after the Dissolution of the Soviet Union, many of these Russian scientists left their native country for working in foreign institutions, where they still continue their studies of autowaves.

[A: 17][A: 18] A huge role in the study of autowave models of cardiac tissue belongs to Denis Noble and members of his team from the University of Oxford.

has in it a very complex form of two intersecting parabolas, besides more crossed with two straight lines, resulting in a more pronounced nonlinear properties of this model.

Autowaves is an example of a self-sustaining wave process in extensive nonlinear systems containing distributed energy sources.

However, in the 21st century, researchers began to discover a growing number of examples of self-wave solutions when the "classical" principle is violated.

There are a great deal of other natural objects that are also considered among autowave processes: oscillatory chemical reactions in active media (e.g., Belousov–Zhabotinsky reaction), the spread of excitation pulses along nerve fibres, wave chemical signalling in the colonies of certain microorganisms, autowaves in ferroelectric and semiconductor films, population waves, spread of epidemics and of genes, and many other phenomena.

Nerve impulses, which serve as a typical example of autowaves in an active medium with recovery, were studied as far back as 1850 by Hermann von Helmholtz.

The properties of nerve impulses that are typical for the simplest self-wave solutions (universal shape and amplitude, independent of the initial conditions, and annihilation under collisions) were ascertained in the 1920s and 1930s.

Consider a 2D active medium consisting of elements, each of which can be found in three different states: rest, excitation and refractoriness.

Unique opportunities to study the autowave processes in two- and three-dimensional active media with very different kinetics are provided with methods of mathematical modelling using computers.

First of all, the elements of the active media can be, at least, of three very different types; these are self-exciting, excitable and trigger (or bistable) regimes.

A bistable element has two stable stationary states, transitions between which occur when external influence exceeds a certain threshold.

A self-oscillating element has no stationary states and continually performs stable oscillations of some fixed form, amplitude and frequency.

An example of a self-oscillating medium is the SA node in the heart, in which excitation pulses arise spontaneously.

that a significant difference between these three types of behaviour of an active medium is caused by the quantity and the position of its singular points.

The shape of autowaves observed in reality can be very similar to each other, and therefore it can be difficult to assess the type of element only by the form of the excitation pulse.

Besides, autowave phenomena, which can be observed and investigated, depend greatly on geometrical and topological peculiarities of an active medium.

In such a way, it is distinguished at least five type of re-entry,[note 2] which are running around the ring, spiral wave, reverberator (i.e., two-dimensional autowave vortex) and fibrillation.

The literature identifies two types of sources of concentric autowaves in 2D active media; these are pacemakers and leading centres.

Both the leading centres and reverberators are interesting, because they are not tied to the structure of the medium and can appear and disappear in its different parts.

However, during starvation they crawl together with forming a multicellular organism, which later gives spores that can survive under adverse conditions.

The released quantity of cAMP diffuses through the environment and makes the following cell amoebas "snap into action" by throwing their portion of the morphogen out.

After the passage of the wave, the "discharged" cells begin to accumulate a new portion of cAMP again, due to the synthesis, and after a while they are able to "snap into action" again.Thus, the population of the collective amoebae is a typical example of the active medium.