Variable-order fractional discrete-time recurrent neural networks

• Published in: Journal of computational and applied mathematics Vol. 370; p. 112633
• Main Authors: Huang, Lan-Lan, Park, Ju H., Wu, Guo-Cheng, Mo, Zhi-Wen
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.05.2020
• Subjects: Fractional discrete-time systems; Recurrent neural networks; Short memory; Variable-order modeling; Short memory; Recurrent neural networks; Fractional discrete-time systems; Variable-order modeling
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2019.112633

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.