Examining the Chaotic Behavior in Dynamical Systems by Means of the 0-1 Test

Abstract

We perform the stability analysis and we study the chaotic behavior of dynamical systems, which depict the 3-particle Toda lattice truncations through the lens of the 0-1 test, proposed by Gottwald and Melbourne. We prove that the new test applies successfully and with good accuracy in most of the cases we investigated. We perform some comparisons of the well-known maximum Lyapunov characteristic number method with the 0-1 method, and we claim that 0-1 test can be subsidiary to the LCN method. The 0-1 test is a very efficient method for studying highly chaotic Hamiltonian systems of the kind we study in our paper and is particularly useful in characterizing the transition from regularity to chaos.