Tv. Dmitrieva et Nm. Ryskin, Complex dynamics and chaos in the parametric coupling of counter-propagating waves, J EXP TH PH, 89(5), 1999, pp. 1015-1020
We study the dynamics of a distributed self-oscillating system of three par
ametrically coupled waves, one of which is propagating counter to the other
two. We show that an infinite number of natural modes are self-excited as
the bifurcation parameter, which has the meaning of the pump amplitude, inc
reases without bound. Exact solutions describing steady-state oscillation r
egimes are found. We present the results of computer simulation, which show
that for moderate pump amplitudes the transient process terminates when a
stationary state corresponding to the fundamental mode sets in. As supercri
ticality increases, the oscillations become chaotic, with the transition to
chaos being rapid. We note an analogy that exists between the dynamics of
such a system and the dynamics of a Lorentz system. (C) 1999 American Insti
tute of Physics. [S1063-7761(99)02611-6].