Fold-Fold Singularity in a Piecewise Smooth Mathematical Model Describing the Dynamics of a Stockless Market

Abstract

Fold-fold singularities are critical points or singularities in piecewise smooth dynamical systems (PWS) where both the stability and the structure of the system change. These singularities are of great importance in the study of specific dynamics, such as those in markets, as they indicate significant transformations in their evolution, including sudden variability in prices or changes in the behavior of offers and demand. Despite the substantial increase in the use of mathematical and computational tools applied to market dynamics, the current literature does not thoroughly address the study of the existence of fold-fold singularities in piecewise smooth systems within this context. Therefore, due to the importance of markets as economic activities, this paper proves the existence of such a singularity in a mathematical model that describes the dynamics of a stockless market, which is represented by a system of ordinary differential equations defined with piecewise smooth functions.