How to detect Wada basins

Wagemakers, Alexandre; Daza, Álvar; Sanjuán, Miguel A. F.

doi:10.3934/dcdsb.2020330

Cited by 10 publications

(3 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, fractal geometry allows for three or more basins to share a common boundary. Such situation is often referred to as Wada basins, and many works have been devoted to identify, prove and characterize the Wada property [12,[29][30][31]. Its interest resides precisely in the particular uncertainty of these basins: any deviation of an initial condition lying in a Wada boundary can evolve into any of the three or more different fates of the system.…”

Section: Number Of Attractors and Wada Propertymentioning

confidence: 99%

Classifying basins of attraction using the basin entropy

Daza,

Wagemakers,

Sanjuán

2022

Preprint

Self Cite

View full text Add to dashboard Cite

A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most common basins found in nonlinear dynamics with the help of the basin entropy. We have also found interesting connections between the basin entropy and other measures used to characterize the unpredictability associated to the basins of attraction, such as the uncertainty exponent, the lacunarity or other different parameters related to the Wada property.

show abstract

Section: Number Of Attractors and Wada Propertymentioning

confidence: 99%

Classifying basins of attraction using the basin entropy

Daza,

Wagemakers,

Sanjuán

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Wagemakers et al commented on these computational methods detecting Wada basins [31]. Daza et al proposed a basin entropy tool to analyze the uncertainty on different Wada basin boundaries [32] and this method are also used to test for fractal boundaries [33] and explosion of basin boundary [34].…”

Section: Introductionmentioning

confidence: 99%

Infinite number of Wada basins in a megastable nonlinear oscillator

Wang

Zhang

2023

Nonlinear Dyn

View full text Add to dashboard Cite

Previous results show that some oscillators possess finite number of Wada basins. Here we find that a nonlinear oscillator can possess a countable infinity of Wada basins and these Wada basins are connected.Infinite number of coexisting attractors and their Wada basins are investigated by the basin cell theorem and generalized basin cell theorem. Infinite number of Wada basins are systematic, which identical basins structure can be identified in each periodic X-axis coordinate interval. This type of Wada basin boundary can lead to a high level of indeterminacy and an extreme sensitive dependence on initial condition.

show abstract

“…For further details, see Refs. [16,17], where the state of the art of the Wada property and the current methods to detect it are reviewed.…”

Section: Introductionmentioning

confidence: 99%

Weak dissipation drives and enhances Wada basins in three-dimensional chaotic scattering

Fernández,

Seoane,

Sanjuán

2022

Preprint

View full text Add to dashboard Cite

Chaotic scattering in three dimensions has not received as much attention as in two dimensions so far. In this paper, we deal with a three-dimensional open Hamiltonian system whose Wada basin boundaries become non Wada when the critical energy value is surpassed in the absence of dissipation. In particular, we study here the dissipation effects on this topological change, which has no analogy in two dimensions. Hence, we find that non-Wada basins, expected in the absence of dissipation, transform themselves into partially Wada basins when a weak dissipation reduces the system energy below the critical energy. We provide numerical evidence of the emergence of the Wada points on the basin boundaries under weak dissipation. According to the paper findings, Wada basins are typically driven, enhanced and, consequently, structurally stable under weak dissipation in three-dimensional open Hamiltonian systems.

show abstract

How to detect Wada basins

Cited by 10 publications

References 32 publications

Classifying basins of attraction using the basin entropy

Classifying basins of attraction using the basin entropy

Infinite number of Wada basins in a megastable nonlinear oscillator

Weak dissipation drives and enhances Wada basins in three-dimensional chaotic scattering

Contact Info

Product

Resources

About