Multiscale dynamics and robust critical scaling in a continuum current sheet model.
We analyze the self-organized critical behavior of a continuum running avalanche model. We demonstrate that over local interaction scales, the model behavior is affected by low-dimensional chaotic dynamics that plays the role of the primary noise source. With the help of scale-free avalanches, the uncertainty associated with chaos is distributed over a variety of intermediate scales and thus gives rise to spatiotemporal fluctuations that are characterized by power-law distribution functions. We show that globally, the continuum model displays structurally stable critical scaling that can be observed in a finite region in the control parameter space. In this region, the system exhibits a power-law critical divergence of the integrated response function over a broad range of dissipation rates. The observed behavior involves a remarkably stable spatial configuration. We explain the robust features of the model by the adjustable dynamics of its global loading-unloading cycle, which allows maintaining the long-term stationary state without affecting the intrinsic avalanche dynamics.