Relation between HVG-irreversibility and persistence in the modified Langevin equation

Abstract

In this study, we investigate the relationship between persistence/antipersistence and time-irreversibility by using the Kullback-Leibler Divergence (KLD) in the directed Horizontal Visibility Graph applied to a new modified Langevin equation with persistence parameter d. A non-trivial relationship KLD(d) was found, characterized by a non-symmetric shape, which suggests that time-irreversibility increases with the degree of persistence or antipersistence. The analysis is applied to the population growth model, where the level of irreversibility may represent important features of the population dynamics, like its stability and ecosystem health.