To explain the theoretical basis of our model’s analysis, the derivation process of the stochastic averaging method is introduced below.
Consider a quasi-integrable Hamiltonian system under bounded noise excitation governed by the following equations of motion37:
$$\dot{{Q}_{i}}=\frac{\partial H}{\partial {P}_{i} } \,\,\dot{{P}_{i}}=-\frac{\partial H}{\partial {Q}_{i}}-\varepsilon {c}_{ij}\frac{\partial H}{\partial {P}_{i} }+\varepsilon {h}_{ij}{\xi }_{k}\left(t\right) \,\, i,j=1,…,n;k=1,…,l$$
(1)
where \({Q}_{i}\) and \({P}_{i}\) are the…
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