title: Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays.
abstract: A single inertial BAM neural network with time-varying delays and external inputs is concerned in this paper. First, by choosing suitable variable substitution, the original system can be transformed into first-order differential equations. Then, we present several sufficient conditions for the global exponential stability of the equilibrium by using matrix measure and Halanay inequality, these criteria are simple in form and easy to verify in practice. Furthermore, when employing an error-feedback control term to the response neural network, parallel criteria regarding to the exponential synchronization of the drive-response neural network are also generated. Finally, some examples are given to illustrate our theoretical results.
authors.affiliation: Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Electronic address: jdcao@seu.edu.cn.
authors.forename: Jinde
authors.initials: J
authors.lastname: Cao
authors.affiliation: Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China.
authors.forename: Ying
authors.initials: Y
authors.lastname: Wan
mesh_terms: D000465:Algorithms; D005246:Feedback; D016571:Neural Networks, Computer; D013997:Time Factors
keywords: Global exponential stability; Global synchronization; Inertial BAM neural network; Matrix measure; Time-varying delays