Finite-Time Synchronization of Memristor-Based Fractional Order Cohen-Grossberg Neural Networks

Abstract

This paper is concerned with the finite-time synchronization (FTS) of memristor-based fractional order Cohen-Grossberg neural networks (MFCGNNs) with time-varying delays. Under the frame of fractional order differential inclusion and set-valued map, some new sufficient conditions to guarantee the FTS of MFCGNNs are established by means of constructing two different Lyapunov functions based on L1-norm in Theorem 1 and Lp-norm in Theorem 2. Via applying the asymptotic expansion property of Mittag-Leffler function, we propose a new estimation method of the settling time for synchronization which is less conservative than previous researches. Meanwhile, we deeply discuss the influence factor of settling time for synchronization. Finally, two numerical examples are given to demonstrate the effectiveness of obtained results. INDEX TERMS Memristor-based Cohen-Grossberg neural networks, finite-time synchronization, estimation of the settling time.

Artificial neural networks: a practical review of applications involving fractional calculus

“…Delayed FDE [114] Laplace transform method Delayed competitive FANN Caputo derivative [115] Delayed coupled FANN [84,86,87] Delayed Hopfield FANN [90,[116][117][118] Delayed memristive FANN [119] Delayed memristive BAM FANN [120] Delayed memristive Cohen-Grossberg FANN [121] Delayed quaternion-valued FANN Delayed FDE [98] Laplace This section presents the works found in the review of the state of the art where optimization algorithms are employed for the training of ANN involved with FC. First, the works with a fractional approach are described.…”

“…Finally, in Refs. [120,303], the authors investigated the finite-time projective synchronization of memristive FANN with mixed time-varying delays and uncertain parameters and the finite-time synchronization of memristive Cohen-Grossberg FANN with time-varying delays, respectively. In these works, the Caputo derivative and feedback controllers were applied.…”

Global Mittag-Leffler Synchronization of Fractional-Order Neural Networks With Time-Varying Delay via Hybrid Sliding Mode Control

“…In [9], fractional-order chaotic systems with completely unknown dynamics and structure are proposed to study power systems. Recently, based on the unique advantages of fractional calculus, fractional-order neural networks (FNNs), as the popular and important kind of networks, are attracted increasing con-cerns [10], [11], [12], [13], [14], [15]. Among these studies, stability and synchronization of FNNs are always major topics and many sufficient conditions have been proposed for the FNNs with or without time delay.…”