Journal
NEURAL NETWORKS
Volume 122, Issue -, Pages 382-394Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.neunet.2019.11.004
Keywords
Mittag-Leffler stability; Discrete-time; Synchronization; Fractional-order complex-valued neural networks; Lyapunov's direct method; Time delay
Funding
- National Natural Science Foundation of China [61773004, 61803056, 61906023]
- Program of Chongqing Innovation Team Project in University, China [CXTDX201601022]
- Chongqing Research Program of Basic Research and Frontier Technology, China [cstc2018jcyjAX0365, cstc2019jcyj-msxmX0722, cstc2019jcyj-msxmX0710]
- Graduate Scientific Research and Innovation Foundation, China Project of Chongqing [CYS18234]
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Without decomposing complex-valued systems into real-valued systems, this paper investigates existence, uniqueness, global Mittag-Leffler stability and global Mittag-Leffler synchronization of discrete-time fractional-order complex-valued neural networks (FCVNNs) with time delay. Inspired by Lyapunov's direct method on continuous-time systems, a class of discrete-time FCVNNs is further discussed by employing the fractional-order extension of Lyapunov's direct method. Firstly, by means of contraction mapping theory and Cauchy's inequality, a sufficient condition is presented to ascertain the existence and uniqueness of the equilibrium point for discrete-time FCVNNs. Then, based on the theory of discrete fractional calculus, discrete Laplace transform, the theory of complex functions and discrete Mittag-Leffler functions, a sufficient condition is established for global Mittag-Leffler stability of the proposed networks. Additionally, by applying the Lyapunov's direct method and designing a effective control scheme, the sufficient criterion is derived to ensure the global Mittag-Leffler synchronization of discrete-time FCVNNs. Finally, two numerical examples are also presented to manifest the feasibility and validity of the obtained results. (c) 2019 Elsevier Ltd. All rights reserved.
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