In this paper we address practical aspects of the implementation of the 0–1 test for chaos in
deterministic systems. In addition, we present a new formulation of the test which …

We present a survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for
dynamical systems, as well as of the numerical techniques developed for the computation of …

Artificial neural networks are universal function approximators. They can forecast dynamics,
but they may need impractically many neurons to do so, especially if the dynamics is chaotic …

We investigate the detailed dynamics of multi-dimensional Hamiltonian systems by studying
the evolution of volume elements formed by unit deviation vectors about their orbits. The …

We use the smaller alignment index (SALI) to distinguish rapidly and with certainty between
ordered and chaotic motion in Hamiltonian flows. This distinction is based on the different …

Intramolecular vibrational energy redistribution (IVR) impacts the dynamics of reactions in a
profound way. Theoretical and experimental studies are increasingly indicating that …

The rapid growth of research in exploiting machine learning to predict chaotic systems has
revived a recent interest in Hamiltonian neural networks (HNNs) with physical constraints …

Chaotic nonlinear systems are systems whose main feature is extreme sensitivity to noise in
the problem or the corresponding initial conditions. In this paper, we examine the chaotic …

The reader can find in the literature a lot of different techniques to study the dynamics of a
given system and also, many suitable numerical integrators to compute them …

In this paper we study briefly several chaos indicators and we focus our attention on the
recently developed, presenting a numerical scheme for its calculation based on the Taylor …