Model Fibrillation as an Analogue of the Hyperbolic the Smale-Williams Attractor| Biomed Grid

Currently, active media form a very promising area of research, because they include a variety of physical, chemical, biological, etc. objects: electronic solid-state systems, a number of chemical solutions and gels (including the Belousov reaction), nerve and muscle tissue, microbial colonies, ecological systems, etc. Representation of active media through ensembles linked excitable or self-oscillating elements is quite useful method of analysis, because the active media allows you to deeply understand the basic dynamic processes occurring in such environments. As is known, this approach goes back to the Wiener and rosenbluth Model [1], according to which the excitable medium consists of a set of interacting elements in one of three possible States: excitation, refractoriness or rest. Later, models such as limit-cycle oscillators and chaotic maps [2-3] also began to play an important role not only in a fairly realistic description of active media, but also in understanding the possible behavior of systems far from equilibrium. Many useful concepts, such as phase captures, synchronization, and space-time chaos, have become popular due to detailed studies of similar nonlinear models [4-6]. Analysis of systems of interacting elements allows us to determine a number of patterns of behavior of active environments, often hidden and implicit. For example, it becomes possible to describe complex (including chaotic) dynamic regimes at a qualitatively different level, to calculate a number of invariant characteristics of the process dynamics and to give a visual representation of the obtained solution.