ИСТИНА

Spatio-temporal patterns formed in systems far from thermodynamic equilibrium are widely spread in nature. They are observed in systems of different nature: physical, chemical, biological. In experiments two major types of spatially non-uniform structures are observed: non-localized patterns that occupy the whole available space, and localized structures, that do not spread far away from the place of their origin. While in the region of Turing instability non-localized dissipative structures are always formed, localized structures can arise rigidly in the prebifurcation region of subcritical Turing instability due to large enough initial local excitation. Under appropriate parameter values, these structures may evolve into non-localized ones due to perturbations. We investigate numerically the behavior of a two-component reaction-diffusion system of FitzHugh-Nagumo type before the onset of subcritical Turing bifurcation in one- and two-dimensional cases in response to local rigid perturbation. In a large region of parameters, initial perturbation evolves into a localized structure. In a part of that region, closer to the bifurcation line, this structure turns out to be unstable and undergoes self-completion covering all the available space in course of time. Depending on the parameter values in two-dimensional space this process happens either through generation and evolution of new structures or through the elongation, deformation and rupture of initial structure, leading to space-filling non-branching snake-like patterns. Transient regimes are also possible.