  The statistical properties of the phases of several modes nonlinearly coupled
in a random system are investigated by means of a Hamiltonian model with
disordered couplings. The regime in which the modes have a stationary
distribution of their energies and the phases are coupled is studied for
arbitrary degrees of randomness and energy. The complexity versus temperature
and strength of nonlinearity is calculated. A phase diagram is derived in terms
of the stored energy and amount of disorder. Implications in random lasing,
nonlinear wave propagation and finite temperature Bose-Einstein condensation
are discussed.
