Spectral density analysis of nonlinear hysteretic systems.

A method for the analysis of spectral densities of hysteretic nonlinearities driven by diffusion processes is presented. This method is based on the Preisach formalism for the description of hysteresis and the mathematical machinery of diffusion processes on graphs. The calculations are appreciably simplified by the introduction of the "effective" distribution function. The implementation of the method for the case of the Ornstein-Uhlenbeck input process is presented in detail, and analytical expressions for spectral noise densities for various hysteretic systems are obtained. The general qualitative features of these spectral densities are examined and their dependence on various parameters is discussed. Because of the universality of the Preisach model, this approach can be used to compute spectra in hysteresis nonlinearities of various physical origins.