Complex dynamics and chaos in the parametric coupling of counter-propagating waves

We study the dynamics of a distributed self-oscillating system of three parametrically 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, increases without bound. Exact solutions describing steady-state oscillation regimes 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 supercriticality 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. Zh. éksp. Teor. Fiz. 116, 1871–1881 (November 1999)