  We study the phase synchronized clusters in the diffusively coupled maps on
the Cayley tree networks for heterogeneous delay values. Cayley tree networks
comprise of two parts: the inner nodes and the boundary nodes. We find that
heterogeneous delays lead to various cluster states, such as; (a) cluster state
consisting of inner nodes and boundary nodes, and (b) cluster state consisting
of only boundary nodes. The former state may comprise of nodes from all the
generations forming self-organized cluster or nodes from few generations
yielding driven clusters depending upon on the parity of heterogeneous delay
values. Furthermore, heterogeneity in delays leads to the lag synchronization
between the siblings lying on the boundary by destroying the exact
synchronization among them. The time lag being equal to the difference in the
delay values. The Lyapunov function analysis sheds light on the destruction of
the exact synchrony among the last generation nodes. To the end we discuss the
relevance of our results with respect to their applications in the family
business as well as in understanding the occurrence of genetic diseases.
