Irreversible Hysteresis of Internal Structure of Tangle Dissipative Optical Solitons

For three-dimensional tangle laser solitons that have a number of unclosed and closed vortex lines and coexist in a range of the scheme parameters, we predict irreversible hysteretic transformation of their internal structure when a system parameter slowly and regularly varies crossing the boundary of the stability of one or another soliton. During the hysteresis cycle, when restoring the initial parameter value, the soliton topology simplifies (decrease of topological indices), its field energy decreases, and the energy of the medium increases. The transient includes a series of elementary reactions: reconnection of vortex lines, separation of closed vortex loops after strong bending of a parent vortex line, and twist of unclosed vortex lines changing topological indices. During the transient, new (metastable) types of localized topological structures arise. It is shown that the tangent energy flow along closed vortex lines is unidirectional or direction alternating.