By using analytical and numerical methods the authors study one of the basic models of mathematical physics—the so-called complex Ginzburg-Landau equation [Formula: see text] with the provision that no fluxes exist at the segment boundaries. A new class of solutions is found for this equation. It is shown that among its solutions there are analogs of limiting cycles of the second kind. A value describing these analogs is introduced, and a scenario of its variation depending on the parameters of the problem is given. A new type of spontaneous appearance of symmetry is shown when we go from initial data in the general form to spatially symmetrical solutions describing quasiperiodic regimes.
Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems