Abstract
This work principally considers the stability issue and the emergence of Hopf bifurcation for a class of fractional-order BAM neural network models concerning time delays. Through the detailed analysis on the distribution of the roots of the characteristic equation of the involved fractional-order delayed BAM neural network systems, we set up a new delay-independent condition to guarantee the stability and the emergence of Hopf bifurcation for the investigated fractional-order delayed BAM neural network systems. The work indicates that delay is a significant element that has a vital impact on the stability and the emergence of Hopf bifurcation in fractional-order delayed BAM neural network systems. The simulation figures and bifurcation plots are clearly presented to verify the derived key research results. The established conclusions of this work have significant guiding value in regulating and optimizing neural networks.
Highlights
Neural networks have been found to have immense application prospect in a lot of subject areas such as modeling human brain, remote sensing, biological science, pattern recognition, artificial intelligence, and control technique [1, 2]
Time delay often occurs in neural network systems due to the lag of the response of signal transmission of the neurons in neural networks. us, it is necessary for us to establish the delayed neural networks to describe the real situation of neural networks
Maharajan et al [7] set up a new global robust exponential stability condition for a class of uncertain BAM neural network systems involving mixed time delays
Summary
Neural networks have been found to have immense application prospect in a lot of subject areas such as modeling human brain, remote sensing, biological science, pattern recognition, artificial intelligence, and control technique [1, 2]. In order to grasp the effect of time delay on various dynamical properties of neural networks, miscellaneous delayed neural networks have been built and studied. Ge and Xu [16] obtained the sufficient condition to ensure the stability and the onset of Hopf bifurcation for delayed neural networks involving four neurons. Yang and Ye [17] dealt with the stability and bifurcation behavior for delayed BAM neural network involving five neurons. It is a pity that a great deal of works is only concerned with delayinduced Hopf bifurcation for integer-order dynamical system concerning delays and few publications focus on the fractional-order case (see [30, 31]). Is viewpoint stimulates us to deal with the delay-induced Hopf bifurcation of delayed neural networks involving multiple neurons.
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