Overview of the advances in understanding chaos in low-dimensional dynamical systems subjected to parameter drift

Jánosi, Dániel; Tél, Tamás

doi:10.1016/j.physrep.2024.09.003

Physics Reports

2024

DOI: 10.1016/j.physrep.2024.09.003

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Overview of the advances in understanding chaos in low-dimensional dynamical systems subjected to parameter drift

Dániel Jánosi,

Tamás Tél

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2024

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Cited by 2 publications

References 154 publications

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Orbital dynamics in galactic potentials under mass transfer

Illés,

Jánosi,

Kovács

2024

A&A

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Context. Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes such as star formation and merging events. Recent studies show that an ensemble approach along with the so-called snapshot framework in the theory of dynamical systems provide a powerful tool to analyze the time-dependent dynamics. Aims. In this work, we aim to explore and quantify the phase space structure and dynamical complexity in time-dependent galactic potentials consisting of multiple components. Methods. We applied the classical method of Poincaré surface of sections to analyze the phase space structure in a chaotic Hamiltonian system subjected to parameter drift. This, however, makes sense only when the evolution of a large ensemble of initial conditions is followed. Numerical simulations explore the phase space structure of such ensembles while the system undergoes a continuous parameter change. The pair-wise average distance of ensemble members allowed us to define a generalized Lyapunov exponent, which might also be time-dependent, to describe the system stability. Results. We provide a comprehensive dynamical analysis of the system under circumstances where linear mass transfer occurs between the disk and bulge components of the model.

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Orbital dynamics in galactic potentials under mass transfer

Illés,

Jánosi,

Kovács

2024

A&A

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Magnetic structures in the explicitly time-dependent nontwist map

Jánosi,

Horváth,

Édes

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate how the magnetic structures of the plasma change in a large aspect ratio tokamak perturbed by an ergodic magnetic limiter, when a system parameter is non-adiabatically varied in time. We model such a scenario by considering the Ullmann–Caldas nontwist map, where we introduce an explicit time-dependence to the ratio of the limiter and plasma currents. We apply the tools developed recently in the field of chaotic Hamiltonian systems subjected to parameter drift. Namely, we follow trajectory ensembles initially forming Kolmogorov Arnold Moser (KAM) tori and island chains in the autonomous configuration space. With a varying parameter, these ensembles, called snapshot tori, develop time-dependent shapes. An analysis of the time evolution of the average distance of point pairs in such an ensemble reveals that snapshot tori go through a transition to chaos, with a positive Lyapunov exponent. We find empirical power-law relationships between both the Lyapunov exponent and the beginning of the transition to chaos (the so-called critical instant), as a function of the rate of the parameter drift, with the former showing an increasing trend and the latter a decreasing trend. We conclude that, in general, coherent tori and magnetic islands tend to break up and become chaotic as the perturbation increases, similar to the case of subsequent constant perturbations. However, because of the continuous drift, some structures can persist longer and exist even at perturbation values where they would not be observable in the constant perturbation case.

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Overview of the advances in understanding chaos in low-dimensional dynamical systems subjected to parameter drift

Cited by 2 publications

References 154 publications

Orbital dynamics in galactic potentials under mass transfer

Orbital dynamics in galactic potentials under mass transfer

Magnetic structures in the explicitly time-dependent nontwist map

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