Stochastic self-modulation of waves in nonequilibrium media

The paper reports the discovery and investigation, through a qualitative analysis and a numerical experiment, of a stochasticity that arises as a result of the development of modulation instability in a nonequilibrium dissipative medium with a spectrally narrow amplification increment. A detailed investigation is camed out of a three-mode model describing the modulation decay of a pair of quanta in the same state into a symmetric pair (20, = o+ + o-) under the assumption that the o, quanta are produced because the medium is in a nonequilibrium state, while the o* quanta disappear because of dissipation. The phase space of this system is found to contain an attracting set (attractor), on which the motion of the system is aperiodic, and which describes a complex dynamics. The Poincark map corresponding to this attractor is similar to the well-known extension mapping of a segment into itself. The structure of the attractor is of the Cantor type, and the motion on it is characterized by a contiowus spectmm.