Effect of stochasticity on targeted energy transfer from a linear medium to a strongly nonlinear attachment

In this work the problem of targeted energy transfer (TET) from a linear medium to a nonlinear attachment is studied in the presence of stochasticity. Using a Green’s function formulation, complexification-averaging technique and diffusion approximation we derive a complex, nonlinear, Ito stochastic differential equation that governs the slow dynamics of the system. Through the numerical solution of the corresponding Fokker–Planck–Kolmogorov (FPK) equation we study the optimal regime of TET and its robustness to stochasticity for the case of nonlinear interactions of the nonlinear attachment with a single mode of the linear system. The probabilistic analysis reveals that in the presence of stochasticity the optimal TET regime, predicted in the deterministic theory, is not only preserved but also is enhanced due to the interaction of nonlinearity and stochasticity.