Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks

• Published in: Neural networks Vol. 104; pp. 104 - 113
• Main Authors: Yang, Shuai, Yu, Juan, Hu, Cheng, Jiang, Haijun
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.08.2018
• Subjects: Complex-valued neural network; Fractional-order derivative; Linear feedback control; Quasi-projective synchronization; Linear feedback control; Quasi-projective synchronization; Complex-valued neural network; Fractional-order derivative
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2018.04.007

In this paper, without separating the complex-valued neural networks into two real-valued systems, the quasi-projective synchronization of fractional-order complex-valued neural networks is investigated. First, two new fractional-order inequalities are established by using the theory of complex functions, Laplace transform and Mittag-Leffler functions, which generalize traditional inequalities with the first-order derivative in the real domain. Additionally, different from hybrid control schemes given in the previous work concerning the projective synchronization, a simple and linear control strategy is designed in this paper and several criteria are derived to ensure quasi-projective synchronization of the complex-valued neural networks with fractional-order based on the established fractional-order inequalities and the theory of complex functions. Moreover, the error bounds of quasi-projective synchronization are estimated. Especially, some conditions are also presented for the Mittag-Leffler synchronization of the addressed neural networks. Finally, some numerical examples with simulations are provided to show the effectiveness of the derived theoretical results.