title: Global O(t(-α)) stability and global asymptotical periodicity for a non-autonomous fractional-order neural networks with time-varying delays.
abstract: The present paper studies global O(t(-α)) stability and global asymptotical periodicity for a non-autonomous fractional-order neural networks with time-varying delays (FDNN). Firstly, some sufficient conditions are established to ensure that a non-autonomous FDNN is global O(t(-α)) stable based on a new Lyapunov function method and Leibniz rule for fractional differentiation. Next it is shown that the periodic or autonomous FDNN cannot generate exactly nonconstant periodic solution under any circumstances. Finally, we show that all solutions converge to a same periodic function for a periodic FDNN by using a fractional-order differential inequality technique. Our issues, methods and results are all new.
authors.affiliation: College of Mathematics and Statistics, Hubei Normal University, Hubei Huangshi 435002, China. Electronic address: chenbs@email.hbnu.edu.cn.
authors.forename: Boshan
authors.initials: B
authors.lastname: Chen
authors.affiliation: College of Mathematics and Statistics, Hubei Normal University, Hubei Huangshi 435002, China; School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China. Electronic address: chenjiejie118@gmail.com.
authors.forename: Jiejie
authors.initials: J
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D015233:Models, Statistical; D016571:Neural Networks, Computer; D010507:Periodicity; D013997:Time Factors
keywords: Fractional-order neural networks; Global  stability; Globally S-asymptotic periodicity; S-asymptotically periodic solution; Time-varying delays