相关论文: The Fast Norm Vector Indicator (FNVI) method: A ne…

A new dynamical parameter, the f-indicator, is introduced and used in order to distinguish between regular and chaotic motion in galactic Hamiltonian systems. Two kinds of galactic potentials are used: (i) a global potential, which…

We introduce a new methodology for a fast and reliable discrimination between ordered and chaotic orbits in multidimensional Hamiltonian systems which we call the Linear Dependence Index (LDI). The new method is based on the recently…

In this paper, we explore the application of Machine Learning techniques, specifically Support Vector Machines (SVM), to unveil the chaotic and regular nature of trajectories in Hamiltonian systems using Lagrangian descriptors. Traditional…

Using the tools of Differential Geometry, we define a new <<fast>> chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e. "quickly") than the usual tools, like Lyapunov Characteristic Numbers…

To determine the regular or chaotic nature of the orbits in dynamical systems can be quite an issue. In this article, following Vozikis et al. (2000), we propose a new tool, namely, the Power Spectrum Indicator (PSI), $\psi^2$, that enables…

The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…

The recently introduced GALI method is used for rapidly detecting chaos, determining the dimensionality of regular motion and predicting slow diffusion in multi--dimensional Hamiltonian systems. We propose an efficient computation of 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 behavior of the SALI for the two cases: the index…

The Smaller Alignment Index (SALI) is a very useful and efficient indicator that can distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian systems. This is based on the different behavior of the SALI in…

The recurrence-based divergence quantifier ($DIV$), traditionally applied to dissipative systems, is shown here to be an effective finite-time chaos indicator for conservative dynamics. We benchmark its performances against the…

We present a method for the computation of the Generalized Alignment Index (GALI), a fast and effective chaos indicator, using a multi-particle approach that avoids variational equations. We show that this approach is robust and accurate by…

Recently, we have demonstrated that our approach is a highly effective tool while analysing complex phenomena existing in networks of coupled nonlinear systems. In the present article we present the results of our investigations into a…

A signal processing method designed for the detection of linear (coherent) behaviors among random fluctuations is presented. It is dedicated to the study of data recorded from nonlinear physical systems. More precisely the method is suited…

A recently introduced chaos detection method, the Relative Lyapunov Indicator (RLI) is investigated in the cases of symplectic mappings and continuous Hamiltonian systems. It is shown that the RLI is an efficient numerical tool in…

We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular,…

In this paper we introduce a chaos indicator derivable from Lagrangian descriptors (LDs), defined as the difference in LD values between two neighboring trajectories. This difference LD is remarkably easy to implement and interpret,…

We present and validate simple and efficient methods to estimate the chaoticity of orbits in low dimensional dynamical systems from computations of Lagrangian descriptors (LDs) on short time scales. Two quantities are proposed for…

A fractal method to detect, locate and quantify chaos in multi-dimensional-conservative-closed systems, based on the creation of artificial exits, is presented. The method is invariant under space-time changes of coordinates and can be used…

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local…

The understanding of non-linear effects in circular storage rings and colliders based on superconducting magnets is a key issue for the luminosity the beam lifetime optimisation. A detailed analysis of the multidimensional phase space…