The 0-1 Test for Chaos: A Review

Linkage between Ringgit exchange rate and U.S Dollar

“…This paper will implementing the chaotic binary test or also known as 0-1 test [4]. The purpose of this method is to quantify the periodic and non-periodic attractors for chaos detection.…”

“…However, in practice to find the complete trajectory will require more computation time. Furthermore, the dynamic of the trajectory in p-q plane do not only depict the regular (periodic or quasiperiodic dynamics) but also chaotic dynamic that is tends to exhibit the two-dimensional Brownian motion with zero drift and hence evolve diffusively [4]. These dynamics could be conveniently distinguished by using mean square displacement (MSD) that can be computed as follows: The asymptotic growth rate of MSD can be quantify by the value K using two methods;…”

“…However, these methods are complex, random, and give unpredictable result. To name a few, the tests, which have been suggested to identify chaos in time series are entropy and BDS test, Lyapunov exponent, dynamical tool, the correlation dimension, the capacity dimension [10] [16] and 0-1 test by Gottwald and Melbourne [4].…”

“…Due to this difficulty, many researchers have creatively discovered alternative methods to solve this issue. For example, Gottwald and Melboune [4] had proposed 0-1 test method, and Gottwald and Melbourne [3] had compared the Lyaponuv and 0-1 chaotic tests. It was found that 0-1 test is better than Lyapunov test.…”

Dynamical properties of the improved FK3V heart cell model

“…More precisely, this test returns 0 for regular (periodic) and 1 for irregular (chaotic) patterns. The mathematical background can be found in the article by Gottwald and Melbourne, Bernardini and Litak, or in the latest review . This test is applicable on discrete dynamical systems, continuous dynamical systems, and on real data represented as time series .…”