Fractal Dimension Analysis of the Julia Sets of Controlled Brusselator Model
Joint Authors
Deng, Yuqian
Liu, Xiuxiong
Zhang, Yongping
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-11-30
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
Fractal theory is a branch of nonlinear scientific research, and its research object is the irregular geometric form in nature.
On account of the complexity of the fractal set, the traditional Euclidean dimension is no longer applicable and the measurement method of fractal dimension is required.
In the numerous fractal dimension definitions, box-counting dimension is taken to characterize the complexity of Julia set since the calculation of box-counting dimension is relatively achievable.
In this paper, the Julia set of Brusselator model which is a class of reaction diffusion equations from the viewpoint of fractal dynamics is discussed, and the control of the Julia set is researched by feedback control method, optimal control method, and gradient control method, respectively.
Meanwhile, we calculate the box-counting dimension of the Julia set of controlled Brusselator model in each control method, which is used to describe the complexity of the controlled Julia set and the system.
Ultimately we demonstrate the effectiveness of each control method.
American Psychological Association (APA)
Deng, Yuqian& Liu, Xiuxiong& Zhang, Yongping. 2016. Fractal Dimension Analysis of the Julia Sets of Controlled Brusselator Model. Discrete Dynamics in Nature and Society،Vol. 2016, no. 2016, pp.1-13.
https://search.emarefa.net/detail/BIM-1103608
Modern Language Association (MLA)
Deng, Yuqian…[et al.]. Fractal Dimension Analysis of the Julia Sets of Controlled Brusselator Model. Discrete Dynamics in Nature and Society No. 2016 (2016), pp.1-13.
https://search.emarefa.net/detail/BIM-1103608
American Medical Association (AMA)
Deng, Yuqian& Liu, Xiuxiong& Zhang, Yongping. Fractal Dimension Analysis of the Julia Sets of Controlled Brusselator Model. Discrete Dynamics in Nature and Society. 2016. Vol. 2016, no. 2016, pp.1-13.
https://search.emarefa.net/detail/BIM-1103608
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1103608