Predictability of orbits in coupled systems through finite-time Lyapunov exponents

Vallejo, Juan Carlos; Sanjuán, Miguel A. F.

doi:10.1088/1367-2630/15/11/113064

Cited by 17 publications

(8 citation statements)

References 39 publications

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“…Lyapunov Exponents (LEs) describe the asymptotic growth or decay of infinitesimal perturbation acting on the trajectory of a dynamical system. Their finite time estimates, the so-called Finite Time Lyapunov Exponents (FTLEs), refer to stability properties of a specific state of the system with respect to a predefined predictability horizon [22,137,203,258,262]. Large deviations of FTLEs point out extremely stable or unstable states of the system [156] and provide relevant information on its predictability on time scales that are intermediate between the one given by the inverse of the first LE and ultra-long ones [155,180].…”

Section: Large Deviations Of Finite Time Lyapunov Exponentsmentioning

confidence: 99%

Applications of large deviation theory in geophysical fluid dynamics and climate science

et al. 2021

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The climate is a complex, chaotic system with many degrees of freedom. Attaining a deeper level of understanding of climate dynamics is an urgent scientific challenge, given the evolving climate crisis. In statistical physics, many-particle systems are studied using Large Deviation Theory (LDT). A great potential exists for applying LDT to problems in geophysical fluid dynamics and climate science. In particular, LDT allows for understanding the properties of persistent deviations of climatic fields from long-term averages and for associating them to low-frequency, large-scale patterns. Additionally, LDT can be used in conjunction with rare event algorithms to explore rarely visited regions of the phase space. These applications are of key importance to improve our understanding of high-impact weather and climate events. Furthermore, LDT provides tools for evaluating the probability of noise-induced transitions between metastable climate states. This is, in turn, essential for understanding the global stability properties of the system. The goal of this review is manifold. First, we provide an introduction to LDT. We then present the existing literature. Finally, we propose possible lines of future investigations. We hope that this paper will prepare the ground for studies applying LDT to solve problems encountered in climate science and geophysical fluid dynamics.

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Section: Large Deviations Of Finite Time Lyapunov Exponentsmentioning

confidence: 99%

Applications of large deviation theory in geophysical fluid dynamics and climate science

et al. 2021

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“…Different x lead to different estimations, e.g., they have different finite-time Lyapunov exponents λ N (x). Indeed, the distribution of λ N (x) over randomly chosen initial conditions (or computed over the invariant measure of the system) is a characterization of the system and has been used to characterize dynamical trapping [3][4][5][6][7], to test hyperbolicity of the system [8], or to identify small KAM islands [9]. In all these applications, the difficulty is to reliably estimate the tails of the distribution, which typically decay exponentially with λ and N [10].…”

Section: Introductionmentioning

confidence: 99%

Efficiency of Monte Carlo sampling in chaotic systems

2014

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In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on a flat-histogram simulation of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort of the simulation: (i) scales polynomially with the finite-time, a tremendous improvement over the exponential scaling obtained in usual uniform sampling simulations; and (ii) the polynomial scalling is sub-optimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal on the Monte Carlo procedure in chaotic systems. These results remain valid in other methods and show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations.

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“…It therefore indicates how strong the oscillations are around zero. The closer d 0.5 is to 0, the stronger UDV may be present (Vallejo & Sanjuan 2013).…”

Section: Analysis Of the Resultsmentioning

confidence: 98%

Role of dark matter haloes on the predictability of computed orbits

Vallejo

Sanjuán

2016

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Aims. The predictability of a system indicates how often a computed orbit is close to a real orbit of the system, independent of its stability or chaotic nature. We explore the effect of dark halo shapes on the predictability of computed orbits in a Milky Way mean field model. We also present the sources for the low predictability found in some orbits. Methods. We derived a predictability index from the distributions of the finite-time Lyapunov exponents. We computed those distributions and analysed the evolution of their shapes when the finite-time interval sizes are varied. The predictability index can be computed using the interval lengths corresponding to the timescales when the flow dynamics leaves the local regime and enters the global regime. Results. These analyses reveal that not all chaotic orbits have the same predictability and that the predictability of some orbits is more affected than others by the orientation and shape of the dark halo. We show that the lowest predictability may be linked to strong unstable dimension variability.

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Predictability of orbits in coupled systems through finite-time Lyapunov exponents

Cited by 17 publications

References 39 publications

Applications of large deviation theory in geophysical fluid dynamics and climate science

Applications of large deviation theory in geophysical fluid dynamics and climate science

Efficiency of Monte Carlo sampling in chaotic systems

Role of dark matter haloes on the predictability of computed orbits

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