Investigating the Stickiness in a Potential Well

In this work, we use the finite-time Lyapunov exponent (FTLE) for a version of the potential well model with an oscillating bottom. This model is described by a conservative two-dimensional mapping that exhibits a mixed phase space, namely it contains a sea of chaos and the regions of stability. Via FTLE, we show that throughout its orbit, an initial condition in the chaotic sea can become trapped in a certain region. We construct and analyze phase spaces for different ranges of Lyapunov exponents in finite time, highlighting these traps. For smaller and larger values of FTLE, we identified a very regular phase space and a phase space with more chaos. By means of low FTLE values, we observe some small regions in the phase space that present regularities. Therefore, we demonstrate that FTLE can be useful to identify the stickiness effect in a time-dependent potential well.

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Publication Details

Journal
International Journal of Bifurcation and Chaos
Published
2024-09-14
DOI
https://doi.org/10.1142/s021812742430026x
Citations
1
Primary Topic
Hydraulic Fracturing and Reservoir Analysis
Type
article
Field-Weighted Citation Impact
0.21

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article

Investigating the Stickiness in a Potential Well

Diogo Ricardo da Costa, Edson D. Leonel, Antonio Marcos Batista, Juliano A. de Oliveira et al.
1 citations
International Journal of Bifurcation and Chaos
Hydraulic Fracturing and Reservoir Analysis
0.21
article

Investigating the Stickiness in a Potential Well

Diogo Ricardo da Costa, Edson D. Leonel, Antonio Marcos Batista, Juliano A. de Oliveira, José D. Szezech, Flávio Heleno Graciano
article en
1 citations

Abstract

In this work, we use the finite-time Lyapunov exponent (FTLE) for a version of the potential well model with an oscillating bottom. This model is described by a conservative two-dimensional mapping that exhibits a mixed phase space, namely it contains a sea of chaos and the regions of stability. Via FTLE, we show that throughout its orbit, an initial condition in the chaotic sea can become trapped in a certain region. We construct and analyze phase spaces for different ranges of Lyapunov exponents in finite time, highlighting these traps. For smaller and larger values of FTLE, we identified a very regular phase space and a phase space with more chaos. By means of low FTLE values, we observe some small regions in the phase space that present regularities. Therefore, we demonstrate that FTLE can be useful to identify the stickiness effect in a time-dependent potential well.

International Journal of Bifurcation and ChaosVol. 34(13)
Universidade de São Paulo (BR), Centro Universitário da Fundação de Ensino Octávio Bastos (BR), Instituto Federal do Sul de Minas (BR), Universidade Estadual de Ponta Grossa (BR), Universidade Estadual Paulista (Unesp) (BR)
Fundação de Amparo à Pesquisa do Estado de São Paulo, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Financiadora de Estudos e Projetos
Openalex Percentile: Top 52%
Hydraulic Fracturing and Reservoir Analysis
0.21
DOISourceOpenAlex
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Investigating the Stickiness in a Potential Well — Diogo Ricardo da Costa, Edson D. Leonel, et al. · International Journal of Bifurcation and Chaos (2024) | TGRS Research Map | TGRS