Numerical simulations through first order nonlinear difference equation to study highly ductile symmetric fold (HDSF) dynamics: A conceptual study

Abstract

Changes in morphology of a geological fold are due to stress and internally exerting forces (IEFs). Such morphological changes can be quantified in terms of fractal dimensions. Stress and the fractal dimension are depicted in normalized scale as dimensionless parameters.Incorporating these parameters in a first order nonlinear difference equation that has physical relevance as the simplest viable model of a symmetric fold sustaining morphological changes,numerical simulations are carried out which are analogous to creep experiments. In the first experiment, the constant stress (λ) is employed to model the morphological dynamical behaviour of highly ductile symmetric folds (HDSFs) that are postulated as they are precarious to stress and IEF, and will not supervene the state of brittleness during the evolution. In the second experiment, the time dependent stress that is changed according to a dynamical rule is used to model distinct dynamical behaviors of these HDSFs.The results arrived through computer simulations are the attractor interlimb angles (AIAs).Bifurcation diagrams are also depicted to show the dynamical behaviors concerning the change in the stress dynamics.