Cascading effects in the moving Preisach model

We consider jumps in the input-output relationship of a system composed of a Preisach hysteretic transducer and a mean-field type global positive feedback loop. The discontinuities are induced by the feedback loop, which promotes avalanches of cascading flips of the independent domains (spins) in the Preisach model in response to a monotone variation of the input after a moment τ
₀
. We discuss the locations of the avalanches and formulate an Equal Area Rule, which defines their size. Under the assumption that the history of the system prior to the moment τ
₀
has been formed by a stochastic input process, the state of the system at the moment τ
₀
and hence the location and size of the avalanches after this moment become random variables. We present several examples of their distribution.