Statistical characterization and numerical investigation of extreme events in a reduced Belousov-Zhabotinsky reaction model

Abstract

Abstract The Belousov-Zhabotinsky (BZ) reaction model is known for its rich and chaotic dynamics. It can also exhibit extreme events characterized by significant deviations from typical system behavior. This study numerically examines the critical conditions under which extreme events occur in a reduced BZ model. Statistical analysis tools, including probability distribution functions of events and inter-event intervals, are used to analyze the frequency and nature of extreme events in chaotic regimes. Bifurcation diagrams, threshold values, Lyapunov exponents, and state portraits are used to visualize and characterize system transitions. In addition, inter-event intervals are statistically examined, revealing Poisson-like behavior, typical of uncorrelated extreme events. These results provide new insights into the occurrence of rare, high-impact phenomena in chemical reaction models, thus contributing to a better understanding of nonlinear dynamical systems.