Optimization of dynamics indicators in pendular systems

Lyapunov exponents have been utilized extensively in the detection of chaos and stability. Various alternatives, such as finite-time Lyapunov exponents and Lagrangian descriptors, have been recently proposed with the objective of reducing the computational demands of the former. In this study, we introduce a novel indicator inspired by the Lagrangian descriptors for discrete systems. This approach facilitates the exploration and detection of chaos in pendular systems through the discretization of the system using Poincaré sections. A comparison of the results obtained with those from the literature was conducted, yielding successful outcomes. A drawback of those indicators is its high computational burden. An optimization procedure has been successfully implemented. This algorithm reduces the computational time by a factor up to 20 for some indicators. This new procedure outputs favourable results for those indicators that explore large system times.