Morphological Evolution of a Pyramidal Sandpile Through Bifurcation Theory: a Qualitative Model

Abstract

A simple first order nonlinear difference equation that has physical relevance to model the morphological evolution of a pyramidal sandpile is used to simulate distinct possible behaviours. As an attempt to furnish the interplay between numerical experiments and theory of morphological evolution, numerical simulations are performed by iterating this difference equation iterating 3×104 time steps to illustrate several possible morphological dynamical behaviours of a sandpile by changing the regulatory parameter, λ, that explains the detailed form of exodynamic process. Bifurcation diagram is described as a model to illustrate how the sandpile under dynamics behaves concerning change of regulatory parameter. Computed attractor inter-slip face angles (θ∗) at respective threshold regulatory parameters are depicted on the bifurcation diagram. By considering these θ∗s, an equation is also proposed to compute metric universality.