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We study a more general class of the Alessandro-Beatrice-Bertotti-Montorsi(AMMB) models with velocity-dependent dissipation. We obtain the Fokker-Planckequation describing the evolution of an arbitrary initial probabilitydistribution, and from there the stationary distribution under constantdriving. For this class of models, we show that the distribution of the size ofan avalanche is the same as when the dissipation is velocity-independent. Asfor durations, we show that, under non-stationary driving known as "kicks",although no closed-form solution seems to be available for an arbitraryvelocity-dependent dissipation, for large durations the distribution seems todemonstrate an exponential fall-off, while for small durations (under someextra conditions to be made clear in the paper) the distribution seems to showa characteristic power-law behaviour.

Generalizing Alessandro-Beatrice-Bertotti-Montorsi (AMMB) Models to the Case of Velocity-dependent Dissipation