Stochastic resonance with tuning system parameters: The application of bistable systems in signal processing. (Q1401013)

A general bistable dynamic system obeying the stochastic differential equation \[ \dot x_t=a x_t-\mu x_t^3+h_t+ \xi_t, \quad t\geq 0, \;a,\mu>0, \] is considered. Here, \(h\) is an input signal, \(\xi\) is a zero-mean Gaussian noise, \(\langle\xi_0,\xi_t\rangle=2D\delta(t)\), \(D>0\). It is demonstrated (numerically) that for the noise level given, the signal-to-noise ratio can be maximized by choosing \(a\) and \(\mu\) appropriately.