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

Heterogeneous delays making parents synchronized: A coupled maps on Cayley tree model