  Out-of-time-order correlators (OTOC), vigorously being explored as a measure
of quantum chaos and information scrambling, is studied here in the natural and
simplest multi-particle context of bipartite systems. We show that two strongly
chaotic and weakly interacting subsystems display two distinct phases in the
growth of OTOC.The first is dominated by intra-subsystem scrambling, when an
exponential growth with a positive Lyapunov exponent is observed till the
Ehrenfest time. This phase is essentially independent of the interaction, while
the second phase is an interaction dominated exponential approach to saturation
that is universal and described by a random matrix model. This simple random
matrix model of weakly interacting strongly chaotic bipartite systems,
previously employed for studying entanglement and spectral transitions, is
approximately analytically solvable for its OTOC. The example of two coupled
kicked rotors is used to demonstrate the two phases, and the extent to which
the random matrix model is applicable. That the two phases correspond to
delocalization in the subsystems followed by inter-subsystem mixing is seen via
the participation ratio in phase-space. We also point out that the second,
universal, phase alone exists when the observables are in a sense already
scrambled. Thus, while the post-Ehrenfest time OTOC growth is in general not
well-understood, the case of strongly chaotic and weakly coupled systems
presents an, perhaps important, exception.
