Abstract. The paper reviews the works devoted to convex spiral autowaves, which are widely known. Recently a new type of autowaves has been discovered - concave autowaves, they propagate from the periphery of active media to the center and are capable of transfering energy. It is proved that concave spiral  autowaves can exist in specific inhomogeneous active media. Their existence is confirmed by computational experiments. It is established that concave autowaves are widespread in nature. The article gives a more detailed review of the biological and medical applications of spiral concave autowaves,  it is also known that there are many of them in physics, chemistry, hydrodynamics, meteorology, and space. Concave spiral autowaves, carrying energy, are one of the essential tools of self-organization.

 

Key words: convex spiral autowave, concave spiral autowaves, active medium, biomedical applications of concave spiral waves, phase waves in vibrational active media.