Morphological evolution of a pyramidal sandpile through Bifurcation theory: a qualitative model

A simple first order nonlinear difference equation that has physical releva nce to model the morphological evolution of a pyramidal sandpile is used to simulate distinct possible behaviours. As an attempt to furnish the interp lay between numerical experiments and theory of morphological evolution, nu merical simulations are performed by iterating this difference equation ite rating 3 x 10(4) time steps to illustrate several possible morphological dy namical behaviours of a sandpile by changing the regulatory parameter, lamb da, that explains the detailed form of exodynamic process. Bifurcation diag ram is described as a model to illustrate how the sandpile under dynamics b ehaves concerning change of regulatory parameter. Computed attractor inter- slip face angles (theta*) at respective threshold regulatory parameters are depicted on the bifurcation diagram. By considering these theta*s, an equa tion is also proposed to compute metric universality. (C) 1999 Elsevier Sci ence Ltd. All rights reserved.