Influence of Time Delay on Bifurcation in Fractional Order BAM Neural Networks With Four Delays

Abstract

Over the past several decades, numerous scholars have studied the stability and Hopf bifurcation problem of integer-order delayed neural networks. However, the fruits about the stability and Hopf bifurcation for fractional-order delayed neural networks are very scarce. In this paper, we will consider the stability and the existence of Hopf bifurcation of fractional-order bidirectional associative memory (BAM) neural networks with four delays. A set of sufficient criteria to ensure the stability and the existence of Hopf bifurcation for the fractional-order BAM neural networks with four delays are established by choosing the sum of two different delays as a bifurcation parameter. This paper manifests that the delay has an important influence on the stability and Hopf bifurcation of involved networks. An example is displayed to test the rationality of the derived theoretical findings. The derived results of this paper are new and play a key role in optimizing networks and improving human life. INDEX TERMS BAM neural networks, stability, Hopf bifurcation, fractional order, delay.

Comments on “Influence of Time Delay on Bifurcation in Fractional Order BAM Neural Networks With Four Delays”

“…In this comment, the technical calculation error in the main result of the Hopf bifurcation in [1] has been identified and the correct calculation has been presented, which will improve the quality and value of the published work [1].…”

“…As the rest of the paper depends on A 1 (s) and A 2 (s), which rely on the values of a i for i = 1, 2, 3, 4, 5, special attention should be given to these values. For this purpose, the correct value of a 1 = α 1 + α 2 + α 3 should be used in equation ( 7) in [1], which should be followed in the rest of paper [1].…”

“…Recently, neural networks have attracted a significant attention in various research areas owing to their promising application in signal and image processing, optimization solvers, intelligent control, quadratic optimization, and automatic control. In a recent paper [1], the authors discussed that the time delay has an important influence on the stability and Hopf bifurcation of the involved networks. The derived results in this paper are new and will play a key role in the future optimization of networks and the improvement of human life.…”

“…The derived results in this paper are new and will play a key role in the future optimization of networks and the improvement of human life. However, the mathematical modeling discussed in [1] contains a wrong calculation in the early part of the paper related to the Hopf bifurcation, which is subsequently carried out throughout the manuscript. The purpose of this comment is to point out the calculation error in [1] and provide the correct calculation.…”

Stability and Hopf Bifurcation Analysis of a General Tri-diagonal BAM Neural Network with Delays

“…In many artificial neural network models, there is an important two-layer heterogeneous associative network called Bidirectional Associative Memory (BAM) neural network with axon signal transmission delay. Since BAM neural network has potential applications in many fields such as signal processing, pattern recognition and optimization problems [13], it has always been one of the most active areas of research and has attracted many attention of many researchers [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In recent decades, many papers have discussed and studied the BAM neural network, which were first reported by Kosko [14,15].…”