Onset of stochastic synchronization induced by diffusion processes in a generalized Duffing system

In this study, two generalized Duffing systems, which are not directly coupled but subjected to a common stochastic excitation, are studied to address the problem of chaotic synchronization. Three types of stochastic diffusion processes generated by the first-order filter are taken as driving excitations and employed to survey their effects on the onset of synchronization with identical spectral densities but different probability density functions (PDFs). By applying the mean largest Lyapunov exponent, we observe that synchronization can indeed occur in the chaotic Duffing systems when the excitation amplitudes are sufficiently larger than the thresholds needed of the synchronization response. Meanwhile, we show the effects for the three diffusion processes on the onset of synchronization are similar. Above all, the most noteworthy result of this work is that the synchronization thresholds induced by the three diffusion processes are almost identical regardless of the selections of different PDFs. In this sense, the PDFs have almost no influence on the onset of synchronization, while, the threshold amplitudes are merely determined by the spectral densities. This can be comprehended from the view of “energy” since the identical spectral densities of the three diffussion processes embody the same total power.