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We have studied precursors of the global failure in some self-organisedcritical models of sand-pile (in BTW and Manna models) and in the random fiberbundle model (RFB). In both BTW and Manna model, as one adds a small but fixednumber of sand grains (heights) to any central site of the stable pile, thelocal dynamics starts and continues for an average relaxation time (\tau) andan average number of topplings (\Delta) spread over a radial distance (\xi). Wefind that these quantities all depend on the average height (h_{av}) of thepile and they all diverge as (h_{av}) approaches the critical height (h_{c})from below: (\Delta) (\sim (h_{c}-h_{av}))(^{-\delta}), (\tau \sim(h_{c}-h_{av})^{-\gamma}) and (\xi) (\sim) ((h_{c}-h_{av})^{-\nu}). Numericallywe find (\delta \simeq 2.0), (\gamma \simeq 1.2) and (\nu \simeq 1.0) for bothBTW and Manna model in two dimensions. In the strained RFB model we find thatthe breakdown susceptibility (\chi) (giving the differential increment of thenumber of broken fibers due to increase in external load) and the relaxationtime (\tau), both diverge as the applied load or stress (\sigma) approaches thenetwork failure threshold (\sigma_{c}) from below: (\chi) (\sim) ((\sigma_{c})(-)(\sigma)^{-1/2}) and (\tau) (\sim) ((\sigma_{c}) (-)(\sigma)^{-1/2}). Theseself-organised dynamical models of failure therefore show some definiteprecursors with robust power laws long before the failure point. Suchwell-characterised precursors should help predicting the global failure pointof the systems in advance.Comment: 13 pages, 9 figures (eps

Precursors of catastrophe in the Bak-Tang-Wiesenfeld, Manna, and random-fiber-bundle models of failure