Chaos on Set-Valued Dynamics and Control Sets

Román-Flores, Heriberto; Ayala, Víctor

doi:10.5772/intechopen.72232

Cited by 4 publications

(4 citation statements)

References 26 publications

(36 reference statements)

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“…(see [5]). However, in [10,12] the author consider the extention of f to f over the class of compact an convex subsets of a real interval X. In this case, the complexity of f decreases.…”

Section: Theoremmentioning

confidence: 99%

“…According to Bauer et al [4] "The elements of K(X) can be viewed as statistical states, representing imperfect knowledge of the system. The elements of X are imbedded in K(X) as the pure states (see also [12]).…”

Section: Introductionmentioning

confidence: 99%

“…There are many works describing the dynamic behavior of the map f . Some of them analyze the relations between the dynamic of f and those of f , [3], [10],and [12]. In the paper Chain transitivity in hyperspaces, [7], the authors explore which of these topological properties of f are inherited by f , and reciprocally, especially those related to chain transitivity.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamics on Hyperspaces

Ayala¹,

Silva²,

Román-Flores³

2018

Preprint

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Given a compact metric space (X, ) and a continuous function f : X → X, we study the dynamics of the induced map f on the hyperspace of the compact subsets of X. We show how the chain recurrent set of f and its components are related with the one of the induced map. The main result of the paper proves that, under mild conditions, the numbers of chain components of f is greater than the ones of f . Showing the richness in the dynamics of f which cannot be perceived by f .

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“…(see [5]). However, in [10,12] the author consider the extention of f to f over the class of compact an convex subsets of a real interval X. In this case, the complexity of f decreases.…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics on Hyperspaces

Ayala¹,

Silva²,

Román-Flores³

2018

Preprint

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“…It was analyzed that aspects of data center service performance that were mentioned to be key ones [1,2], specifically service transactions index, service resource occupancy index and service performance index. To solve the problem of prediction of those, works were studied devoted to chaotic analysis [2][3][4], radar chart method [1,5] and weighted average method [6]. Also, within the bounds of this study, the fundamental mathematical materials were analyzed [7][8][9] related to fuzzy logic in order to use it at cloud platform data center services performance analysis and prediction.…”

mentioning

confidence: 99%

Development of the performance prediction algorithms for cloud services

Zuev¹,

Kropachev

Usov³

et al. 2018

SRIT

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Main stages of data center service performance prediction were discussed, specifically data monitoring and gathering, calculation and prediction of key indexes and performance index prediction. It was proposed to build data center service performance prediction algorithm based on an analysis of the service transactions index, service resource occupancy index and service performance index. Prediction of the indexes is based on chaotic time series analysis that was used to estimate service transactions index time series trend, the radar chart method to calculate the service resource occupancy index value and weighted average method to calculate service performance index. For performance prediction, it is proposed to use a fuzzy judgment matrix with the service transactions index and service resource occupancy index as input values. It was taken into consideration that service transactions index is usually represented by nonlinear time series and thus the index time series parameters had to be predicted by chaos theory and for the calculation of this index, the estimation procedure of Lyapunov exponent value can be used. The radar chart demonstrates service resource occupancy index estimation of shared storage, mobile storage, memory, computational capability and network bandwidth. The prediction technique was based on the fuzzy nearness category that use input values of transactions index and dynamic changes of the service resource occupancy index.

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Hyperconvergence in topological dynamics

Souza

Alves

2021

Monatsh Math

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Chaos on Set-Valued Dynamics and Control Sets

Cited by 4 publications

References 26 publications

Dynamics on Hyperspaces

Dynamics on Hyperspaces

Development of the performance prediction algorithms for cloud services

Hyperconvergence in topological dynamics

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