Motivated by the latest developments in the dynamics of two, weakly interacting oscillatory chains, as well as, by the recent, ground-breaking achievements in the area of the dynamics of one dimensional granular crystals, we aim at studying the dynamics of the extended model comprising the three, weakly coupled, nonlinear chains - mounted on linear elastic foundations. We establish interesting capacities of the weakly coupled granular chains for recurrent and strong energy exchanges by means of localized waves. In the present study we analyze the governing mechanisms of transition from energy entrapment to the nearly complete, inter-chain energy transport in the system of three coupled, an-harmonic oscillators as well as the oscillatory chains. Two distinct mechanisms leading to the breakdown of energy localization on the first and the second oscillators (oscillatory chains) have been revealed and analyzed in the study. Using the regular multi-scale asymptotic analysis along with the non-smooth temporal transformation procedure (NSTT) we formulate the analytic criteria for the formation of the resonant, inter-chain energy transport. Results of the analytical approximation are in a very good agreement with the results of numerical simulations of the full models.
