Inverse cascade avalanche model with limit cycle exhibiting period doubling, intermittency, and self-similarity

A one-dimensional avalanche "sandpile" algorithm is presented for transport in a driven dissipative confinement system. Sand is added at the closed inflow boundary and redistributed when the local gradient exceeds a threshold. The redistribution rule is conservative, nonlocal, and linear and is chosen to mimic fluid flow. Potential energy is dissipated by avalanches that also expel matter at the open outflow boundary. The system then evolves through an inverse cascade. A "fluidization" parameter L(f) specifies the length scale over which the algorithm operates. The limiting case of L(f)=1 cell and L(f)=N, the system size, are analytically soluble. For other values of L(f) the emergent, large-scale dynamics of the system shows a variety of behavior including a limit cycle that has a period-doubling sequence, intermittency, and a random walk.