Emergence and bifurcations of nonstationary states in the anharmonic oscillator chains

In the present talk I will discuss the mechanism of formation and bifurcations of highly non-stationary regimes manifested by the moderate as well as the intense energy transport emerging in the anharmonic trimer model as well as the coupled granular chains. The basic model under investigation comprises a chain of three coupled anharmonic oscillators given to a localized excitation, where the initial energy is imported solely to the first oscillator. We report the formation of three, basic non-stationary transport states traversed by the locally excited regimes. These states differ one from another by spatial energy distribution as well as the intensity of energy transport along the chain. In the current study we particularly concentrate on the analytical study of the intricate resonant mechanism governing the spontaneous transitions of the locally excited regime between the states. The second part of my talk will be devoted to the passive and semi-active control of spatially extended waves in the system of coupled granular chains. I will mainly focus on the intricate mechanism of the resonant, unidirectional inter-chain wave transfer invoked by the auto-resonant mechanism. Analysis of this peculiar mechanism will be discussed.