Stochastic multiresonance in oscillators induced by bounded noise

Continuity and topological structural stability for nonautonomous random attractors

“…However, in the applications to check condition (5.10) one has to assume that the noise is uniformly bounded as in Remark 7.4, see also [9,19] for more examples of uniformly bounded noises. On the other hand, in Section 7 we provide an example, see Example 7.2, where conditions of Theorem 5.1 are checked, but we do not know if its possible to verify (5.10).…”

“…We also obtain stronger results on the continuity and topological structural stability of nonautonomous random attractors for the case when the random perturbations are uniformly bounded with respect to the random parameter, see Remark 5.4 and Remark 6.3 for more details. Moreover, see [9,25] for examples of this types of noises.…”

Resonance response analysis of nonlinear vibration energy harvesting system under bounded noise excitation

“…Subsequently, the stochastic averaging method was further expanded to discuss the stochastic response characters of the strongly non-linear oscillator under bounded noise excitation with fractional derivative damping [7] and time-delayed feedback [5], respectively. Recently, Bobryk [2] found that the stochastic multiresonance can be induced when a harmonic oscillator has parametric bounded noise and external periodic force. Precisely because the bounded force has made so plentiful dynamics phenomena, particularly the resonant frequencies which can cause greater amplitude than other frequencies, the impact of bounded force on the capture efficiency of VEH system attract more and more public attention.…”