A class of lattice continuous models of self-organized criticality

Abstract

Unlike the conventional case of using cellular automata, we use a system of differential equations to study the self-organized criticality of physical systems. We see that it is not uncommon for some physical quantities, such as power loss, of the system to exhibit 1/f scaling in our new model. Comparison with the original models self-organized criticality (SOC) is also discussed. By means of stochastic lattice differential equations, we can also examine the behavior of the system when the particle addition rate is comparable to the particle dissipation rate which is not allowed by the original models of SOC. Finally, we shall formulate a set of equations using these continuous models to describe a recent experiment done on real sandpiles.