  In this paper we categorize dynamical regimes demonstrated by star-like
networks with chaotic nodes. This analysis is done in view of further studying
of chaotic scale-free networks, since a star-like structure is the main motif
of them. We analyze star-like networks of Henon maps. They are found to
demonstrate a huge diversity of regimes. Varying the coupling strength we
reveal chaos, quasiperiodicity, and periodicity. The nodes can be both fully-
and phase-synchronized. The hub node can be either synchronized with the
subordinate nodes or oscillate separately from fully synchronized subordinates.
There is a range of wild multistability where the zoo of regimes is the most
various. One can hardly predict here even a qualitative nature of the expected
solution, since each perturbation of the coupling strength or initial
conditions results in a new character of dynamics.
