Efficient time series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices

TL;DR

This paper demonstrates that the 0-1 test for chaos is an efficient and reliable method for detecting the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices, outperforming traditional nonlinear time series analysis in terms of computational effort.

Contribution

The study introduces the application of the 0-1 test for chaos to detect the strong stochasticity threshold in anharmonic oscillator chains, showing its effectiveness and computational advantages.

Findings

0-1 test successfully detects the stochasticity threshold.

Conventional methods fail to accurately compute Lyapunov exponents for large data.

0-1 test maintains constant computational effort across energy densities.

Abstract

In this work we study the possibility of detecting the so-called strong stochasticity threshold, i.e. the transition between weak and strong chaos as the energy density of the system is increased, in anharmonic oscillator chains by means of the 0-1 test for chaos. We compare the result of the aforementioned methodology with the scaling behavior of the largest Lyapunov exponent computed by means of tangent space dynamics, that has so far been the most reliable method available to detect the strong stochasticity threshold. We find that indeed the 0-1 test can perform the detection in the range of energy density values studied. Furthermore, we determined that conventional nonlinear time series analysis methods fail to properly compute the largest Lyapounov exponent even for very large data sets, whereas the computational effort of the 0-1 test remains the same in the whole range of values of the energy density considered with moderate size time series. Therefore, our results show that, for a qualitative probing of phase space, the 0-1 test can be an effective tool if its limitations are properly taken into account.