Low-dimensional behavior and symmetry breaking of stochastic systems near criticality-can these effects be observed in space and in the laboratory?
It is demonstrated that nonlinear stochastic systems near criticality (including self-organized criticality) will generally exhibit low-dimensional behavior. A connection is given between the fractal dimensions of finite-dimensional chaotic systems and the anomalous dimensions in stochastic systems near criticality. The effect of additional random noise on stochastic systems will be delineated in terms of the crossover phenomenon between competing criticalities. The possibility of observing such effects in space (such as the onset of substorms) and in the laboratory (such as stochastic particle heating in 'noisy' magnetic fields) is discussed.