Is Weather Chaotic? Coexisting Chaotic and Non-chaotic Attractors Within Lorenz Models

Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xiping; Baik, Jong‐Jin; Faghih-Naini, Sara; Cui, Jialin; Atlas, Robert; Reyes, Tiffany

doi:10.1007/978-3-030-70795-8_57

Cited by 13 publications

(21 citation statements)

References 84 publications

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“…While both the 1963 and 1969 Lorenz models produce various types of solutions [15][16][17], only chaotic and linearly unstable solutions have been a focus. As a result, the concept of finite predictability associated with BE1 and BE3 within specific solutions should be generalized with caution.…”

Section: Discussionmentioning

confidence: 99%

“…The control run has an initial condition of (X, Y, Z) = (0, 1, 0), and the parallel run additionally includes a small perturbation (1 × 10 −10 ) in the initial value of Y. Chaotic solutions in the X-Y-Z phase space within the Lorenz model can be found in Figure 2 of [16].…”

Section: The First Kind Of Butterfly Effect (Be1)mentioning

confidence: 99%

“…Additionally, Prof. Arakawa believed that the predictability limit is not necessarily a fixed number [12]. Recently, the idea of a predictability limit of two weeks has been challenged by new insights obtained using the L63 and L69 models, as well as generalized Lorenz models (e.g., [15][16][17]; and references therein), and promising simulations using advanced models (e.g., [18][19][20][21]).…”

Section: Introductionmentioning

confidence: 99%

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Three Kinds of Butterfly Effects within Lorenz Models

et al. 2022

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Within Lorenz models, the three major kinds of butterfly effects (BEs) are the sensitive dependence on initial conditions (SDIC), the ability of a tiny perturbation to create an organized circulation at large distances, and the hypothetical role of small-scale processes in contributing to finite predictability, referred to as the first, second, and third kinds of butterfly effects (BE1, BE2, and BE3), respectively. A well-accepted definition of the butterfly effect is the BE1 with SDIC, which was rediscovered by Lorenz in 1963. In fact, the use of the term “butterfly” appeared in a conference presentation by Lorenz in 1972, when Lorenz introduced the BE2 as the metaphorical butterfly effect. In 2014, the so-called “real butterfly effect”, which is based on the features of Lorenz’s study in 1969, was introduced as the BE3.

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Section: Discussionmentioning

confidence: 99%

Section: The First Kind Of Butterfly Effect (Be1)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Three Kinds of Butterfly Effects within Lorenz Models

et al. 2022

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“…As the number of dimensions defining the state of a system becomes larger, full characterization of the system’s state becomes more challenging in the real world, leading to chaotic behavior when only a subset of the full features is measured. A well-known example of such a high-dimensional chaotic system is the “butterfly effect” ( Shen et al, 2018 ), which implies that a small perturbation such as (metaphorically) a butterfly flapping its wing can affect the weather at a later time in another place. Consequently, given our lack of awareness of the full feature space, weather predictions remain valid only for a finite time interval such as a few days.…”

Section: Introductionmentioning

confidence: 99%

Single-cell multi-omics and lineage tracing to dissect cell fate decision-making

Haghverdi

Ludwig

2023

Stem Cell Reports

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“…One of the brain's most intriguing traits is its capacity for "Chaos" -the phenomenon whereby straightforward deterministic nonlinear systems exhibit complex unexpected and random -like behavior. Electroencephalogram (EEG) signals [9] are known to have chaotic dynamics [10]. A neural system's sensitivity to little changes in internal functioning characteristics aids in producing the optimal response to various in uences.…”

Section: Introductionmentioning

confidence: 99%

Predicting Ethereum Fraudulency using ChaosNet

Dutta¹,

Ray²

2023

Preprint

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Cryptocurrencies are in high demand right now, perhaps because of their volatile nature and untraceable difficulties. Bitcoin, Ethereum, Dogecoin, and others are just a few. This research seeks to identify falsehoods and probable fraudulences in Ethereum transactional processes. We have provided this capability to ChaosNet, an Artificial Neural Network constructed using Generalized Luroth Series maps. At many spatiotemporal scales, Chaos has been objectively discovered in the brain. Several synthetic neuronal simulations, including the Hindmarsh-Rose model, possess Chaos, and individual brain neurons are known to display chaotic bursting phenomenon. Although Chaos is included in several Artificial Neural Networks (ANNs), for instance, the Recursively Generating Neural Networks, no ANN exist for classical tasks that is fully made up of Chaoticity. ChaosNet uses the chaotic GLS neurons' topological transitivity property to perform classification problems with cutting-edge performance the pool of data including lower training sample count. This synthetic neural network can perform categorization tasks by gathering from a definite amount of training data. ChaosNet utilizes some of the best traits of network subjected to biological neurons, which derive from the strong Chaotic activity of individual neurons, to solve difficult classification tasks on par with or better than standard Artificial Neural Networks. It has been shown to require much fewer training samples.

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Is Weather Chaotic? Coexisting Chaotic and Non-chaotic Attractors Within Lorenz Models

Cited by 13 publications

References 84 publications

Three Kinds of Butterfly Effects within Lorenz Models

Three Kinds of Butterfly Effects within Lorenz Models

Single-cell multi-omics and lineage tracing to dissect cell fate decision-making

Predicting Ethereum Fraudulency using ChaosNet

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