Examining the chaotic behavior in dynamical systems by means of the 0-1 test. (English) Zbl 1243.37060

Zachilas, Loukas; Psarianos, Iacovos N.

J. Appl. Math. 2012, Article ID 681296, 14 p. (2012).

Summary: 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 the 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.

MSC:

37M99	Approximation methods and numerical treatment of dynamical systems
37J35	Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37M10	Time series analysis of dynamical systems
70H06	Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Keywords:

0-1 test; 3-particle Toda lattice truncations; chaotic Hamiltonian systems

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