Appearance of stochasticity on decay limitation of parametric instability

On the basis of analysing the solution of a dynamic system of three waves coupled in reasonance, it is shown that besides the trivial static stabilization mode of parametric instability the stochastic stability mode is possible. In this mode the interacting wave amplitudes being restricted pulsate in time. In the phase space of the dynamic system the trajectories belonging to a so-called strange attractor (SA) correspond to these stochastic motions. It is shown that the SA is analogous to the Lorentz attractor known in hydrodynamics. As a concrete example of a parametric instability restriction, the interaciton of howl and ionic sound in a non-isothermal magnetoactive plasma with plasma oscillations near low hydrid resonance is considered. It is stated that the investigated dynamic system most effectively describes the instability restriction mechanism which leads to the occurence of stochasticity in the system of three interacting waves. The amplitude stochastization takes place in case of a complete phase correlation that is opposite to a frequently used casual phase approximation