Fluctuations in mean-field self-organized criticality
- 40 Downloads
We present two models that exhibit self-organized criticality at the mean-field level. These can be variously interpreted in epidemiological or chemical reaction terms. By studying the master equation for these models we find, however, that only in one of them does the self-organized critical behavior survive in the face of fluctuations. For this model we show the spectrum of the evolution operator to have spectral collapse, i.e., instead of a gap, as would occur in noncritical behavior, there are eigenvalues that approach zero as an inverse power of system size.
Key WordsSelf-organized criticality directed percolation epidemic models chemical reactions transfer matrix spectral collapse
Unable to display preview. Download preview PDF.
- 3.B. Gaveau and L. S. Schulman, Mean-field self-organized criticality,J. Phys. A Lett. 24:L475 (1991).Google Scholar
- 4.L. S. Schulman and P. E. Seiden, Percolation and galaxies,Science 233:425 (1986).Google Scholar
- 5.L. S. Schulman, Modeling galaxies: Cellular automata and percolation, inCellular Automata: Prospects in Astrophysical Applications, A. Lejeune and J. Perdang, eds. (World Scientific, Singapore, 1993).Google Scholar