New Methods of Finite‐Time Synchronization for a Class of Fractional‐Order Delayed Neural Networks

Abstract

Finite-time synchronization for a class of fractional-order delayed neural networks with fractional order , 0 < ≤ 1/2 and 1/2 < < 1, is investigated in this paper. Through the use of Hölder inequality, generalized Bernoulli inequality, and inequality skills, two sufficient conditions are considered to ensure synchronization of fractional-order delayed neural networks in a finitetime interval. Numerical example is given to verify the feasibility of the theoretical results.

Quasi‐Matrix and Quasi‐Inverse‐Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network

“…Neural network has attracted more and more attention since the introduction of fractional calculus and its dynamical behaviors, such as chaos, hyperchaos, bifurcations [20][21][22], existence, stability and consensus [23][24][25][26][27][28][29][30], and control and synchronization [31][32][33][34][35][36][37][38][39][40], have been widely studied. Recently, its synchronization problem has become a research focus and attracted many researchers.…”

“…Recently, its synchronization problem has become a research focus and attracted many researchers. In [32,33], the authors considered the adaptive pinning synchronization and finite time synchronization for delayed fractional order neural network. In [34], He and his cooperators explored quasi-synchronization problem of heterogeneous dynamic networks via distributed impulsive control.…”

Synchronization in Fractional-Order Complex-Valued Delayed Neural Networks

“…Compared with an integer-order model, fractional order models can offer more accurate instrument for memory description and inherited properties of several processes. Some researchers introduced the fractional order derivatives into neural networks; the fractional order neural networks were designed for precisely modelling in real world [ 16 , 17 , 18 , 19 ].…”

Projective synchronization of fractional-order delayed neural networks based on the comparison principle

“…The existence of infinite memory can help fractional-order models better describe the system's dynamical behaviors as illustrated in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Taking these factors into consideration, fractional calculus was introduced to neural networks forming fractional-order neural networks, and some interesting results on synchronization were demonstrated [24][25][26][27][28][29]. Among all kinds of synchronization, projective synchronization, in which the master and slave systems are synchronized up to a scaling factor, is an important concept in both theoretical and practical manners.…”