Gradient Pattern Analysis of Coupled Map Lattices: Insights into Transient and Long-Term Behaviors

Abstract

. Gradient Pattern Analysis (GPA) is a useful technique for analyzing the dynamics of nonlinear 2D-spatiotemporal systems, which is based on the gradient symmetry-breaking properties of a matrix snapshot sequence. GPA has found numerous applications in dynamic systems, particularly in studying logistic Coupled Map Lattices (CMLs) and Swift-Hohenberg amplitude equations. In this work, we propose a new mathematical operation related to the first gradient moment ( G 1 ) defined by the GPA theory. The performance of this new measure is evaluated by applying it to two chaotic CML models (Logistic and Shobu-Ose-Mori). The GPA using the new parameter ( G 1 ) provides a more accurate analysis, allowing the identification of conditions that partially break the gradient symmetry over time. Based on the GPA measurements ( G 1 , G 2 and G 3 ), including a combined analysis with the chaotic parameters, our results demonstrate the potential to analyze chaotic spatiotemporal systems improving our understanding of their underlying dynamics.