title: Analysis of global O(t(-α)) stability and global asymptotical periodicity for a class of fractional-order complex-valued neural networks with time varying delays.
abstract: In this paper, the problem of the global O(t(-α)) stability and global asymptotic periodicity for a class of fractional-order complex-valued neural networks (FCVNNs) with time varying delays is investigated. By constructing suitable Lyapunov functionals and a Leibniz rule for fractional differentiation, some new sufficient conditions are established to ensure that the addressed FCVNNs are globally O(t(-α)) stable. Moreover, some sufficient conditions for the global asymptotic periodicity of the addressed FCVNNs with time varying delays are derived, showing that all solutions converge to the same periodic function. Finally, numerical examples are given to demonstrate the effectiveness and usefulness of our theoretical results.
authors.affiliation: Department of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamil Nadu, India. Electronic address: rakkigru@gmail.com.
authors.forename: R
authors.initials: R
authors.lastname: Rakkiyappan
authors.affiliation: Department of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamil Nadu, India. Electronic address: sivaranjanisurya@gmail.com.
authors.forename: R
authors.initials: R
authors.lastname: Sivaranjani
authors.affiliation: Department of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamil Nadu, India. Electronic address: gvmuruga@gmail.com.
authors.forename: G
authors.initials: G
authors.lastname: Velmurugan
authors.affiliation: Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China. Electronic address: jdcao@seu.edu.cn.
authors.forename: Jinde
authors.initials: J
authors.lastname: Cao
mesh_terms: D000465:Algorithms; D016571:Neural Networks, Computer; D013995:Time
keywords: Complex-valued neural networks; Fractional-order neural networks; Globally asymptotic periodicity; S-asymptotically periodic solution; Time-varying delays