Variable-order fractional discrete-time recurrent neural networks
Discrete fractional calculus is suggested to describe neural networks with memory effects. Fractional discrete-time recurrent neural network is proposed on an isolated time scale. Stability results are investigated via Banach fixed point technique. The attractive solution space is constructed and st...
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| Published in | Journal of computational and applied mathematics Vol. 370; p. 112633 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
15.05.2020
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-0427 1879-1778 |
| DOI | 10.1016/j.cam.2019.112633 |
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| Abstract | Discrete fractional calculus is suggested to describe neural networks with memory effects. Fractional discrete-time recurrent neural network is proposed on an isolated time scale. Stability results are investigated via Banach fixed point technique. The attractive solution space is constructed and stability conditions are provided. Furthermore, short memory and variable-order fractional neural networks are given according to the stability conditions. Two and three dimensional numerical examples are used to demonstrate the theoretical results.
•Variable-order fractional discrete-time neural network is proposed.•Stability conditions are provided by fixed point theorems.•Numerical examples are given to illustrate the theoretical results. |
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| AbstractList | Discrete fractional calculus is suggested to describe neural networks with memory effects. Fractional discrete-time recurrent neural network is proposed on an isolated time scale. Stability results are investigated via Banach fixed point technique. The attractive solution space is constructed and stability conditions are provided. Furthermore, short memory and variable-order fractional neural networks are given according to the stability conditions. Two and three dimensional numerical examples are used to demonstrate the theoretical results.
•Variable-order fractional discrete-time neural network is proposed.•Stability conditions are provided by fixed point theorems.•Numerical examples are given to illustrate the theoretical results. |
| ArticleNumber | 112633 |
| Author | Mo, Zhi-Wen Huang, Lan-Lan Wu, Guo-Cheng Park, Ju H. |
| Author_xml | – sequence: 1 givenname: Lan-Lan surname: Huang fullname: Huang, Lan-Lan email: mathlan@126.com organization: School of Mathematical Science, Sichuan Normal University, Chengdu 610066, Sichuan Province, PR China – sequence: 2 givenname: Ju H. surname: Park fullname: Park, Ju H. email: jessie@ynu.ac.kr organization: Department of Electrical Engineering, Yeungnam University, 280 Daehak–Ro, Kyongsan 38541, Republic of Korea – sequence: 3 givenname: Guo-Cheng orcidid: 0000-0002-1946-6770 surname: Wu fullname: Wu, Guo-Cheng email: wuguocheng@gmail.com organization: Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, PR China – sequence: 4 givenname: Zhi-Wen surname: Mo fullname: Mo, Zhi-Wen organization: School of Mathematical Science, Sichuan Normal University, Chengdu 610066, Sichuan Province, PR China |
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| Title | Variable-order fractional discrete-time recurrent neural networks |
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