  We study two intertwined globally coupled networks of noisy Kuramoto phase
oscillators that have the same natural frequency, but differ in their
perception of the mean field and their contribution to it. Such a give-and-take
mechanism is given by asymmetric in- and out-coupling strengths which can be
both positive and negative. We uncover in this minimal network of networks
intriguing patterns of discordance, where the ensemble splits into two clusters
separated by a constant phase lag. If it differs from $\pi$, then traveling
wave solutions emerge. We observe a second route to traveling waves via
traditional one-cluster states. Bistability is found between the various
collective states. Analytical results and bifurcation diagrams are derived with
a reduced system.
