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A finite (periodic) FPU chain is chosen as a convenient point forinvestigating the energy exchange phenomenon in nonlinear oscillatory systems.As we have recently shown, this phenomenon may occur as a consequence of theresonant interaction between high-frequency nonlinear normal modes. Thisinteraction determines both the complete energy exchange between differentparts of the chain and the transition to energy localization in an excitedgroup of particles. In the paper, we demonstrate that this mechanism can existin realistic (asymmetric) models of atomic or molecular oscillatory chains.Also, we study the resonant interaction of conjugated nonlinear normal modesand prove a possibility of linearization of the equations of motion.  The theoretical constructions developed in this paper are based on theconcepts of "effective particles" and Limiting Phase Trajectories. Inparticular, an analytical description of energy exchange between the "effectiveparticles" in the terms of non-smooth functions is presented. The analyticalresults are confirmed with numerical simulations.

Energy exchange and transition to localization in the asymmetric Fermi-Pasta-Ulam oscilliatory chain