Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks

• Published in: Neural networks Vol. 51; pp. 1 - 8
• Main Authors: Chen, Jiejie, Zeng, Zhigang, Jiang, Ping
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2014; Elsevier
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Computer science; control theory; systems; Connectionism. Neural networks; Differential equations; Electronics; Exact sciences and technology; Filippov’s solution; Fractional-order; Global Mittag-Leffler stability; Integrated circuits; Integrated circuits by function (including memories and processors); Memristor-based neural networks; Micro- and nanoelectromechanical devices (mems/nems); Models, Neurological; Networks; Neural networks; Neural Networks (Computer); Recurrent neural networks; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Stability; Synchronism; Synchronization; Time Factors; Filippov’s solution; Fractional-order; Memristor-based neural networks; Synchronization; Global Mittag-Leffler stability; Recurrent neural nets; Mittag Leffler function; Stability; Differential equation; Lyapunov method; Neural network; Modeling; Fractional derivative; Non volatile memory; Filippov's solution; Memory circuit
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2013.11.016

The present paper introduces memristor-based fractional-order neural networks. The conditions on the global Mittag-Leffler stability and synchronization are established by using Lyapunov method for these networks. The analysis in the paper employs results from the theory of fractional-order differential equations with discontinuous right-hand sides. The obtained results extend and improve some previous works on conventional memristor-based recurrent neural networks. •The fractional-order memristor-based neural networks are discussed in this paper.•We handle the concept solution in the Filippov’s sense for the memristor-based neural networks.•A Lyapunov approach to the stability of fractional-order differential equations is presented in this paper.