Synchronization of Chains of Logistic Maps

We study the synchronisation dynamics of a chain of coupled chaotic maps arranged in a parent-children configuration, with each parent node connected to two children nodes, one of which is also the parent of the next node. We analyse two distinct phenomena: parent-child synchronisation, characterised by the vanishing distance between consecutive nodes, and siblings synchronisation, for which the states of two children coalesce. Our investigation reveals strong differences in the synchronisation mechanisms between these two phenomena, which can be directly linked to the probability distribution of the parent. Theoretical analysis and simulations using the logistic map support our findings. Furthermore, we explore the propagation of perturbations in a synchronised chain by studying the rate of reabsorption of the perturbation.