  We explore the behaviour of chaotic oscillators in hierarchical networks
coupled to an external chaotic system whose intrinsic dynamics is dissimilar to
the other oscillators in the network. Specifically, each oscillator couples to
the mean-field of the oscillators below it in the hierarchy, and couples
diffusively to the oscillator above it in the hierarchy. We find that coupling
to one dissimilar external system manages to suppress the chaotic dynamics of
all the oscillators in the network at sufficiently high coupling strength. This
holds true irrespective of whether the connection to the external system is
direct or indirect through oscillators at another level in the hierarchy.
Investigating the synchronization properties show that the oscillators have the
same steady state at a particular level of hierarchy, whereas the steady state
varies across different hierarchical levels. We quantify the efficacy of
control by estimating the fraction of random initial states that go to fixed
points, a measure analogous to basin stability. These quantitative results
indicate the easy controllability of hierarchical networks of chaotic
oscillators by an external chaotic system, thereby suggesting a potent method
that may help design control strategies.
