2022
DOI: 10.1002/mma.8477
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Further analysis on dynamical properties of fractional‐order bi‐directional associative memory neural networks involving double delays

Abstract: In this study, a class of novel fractional-order bi-directional associative memory (BAM) neural networks involving double time delays are put up and investigated. First of all, we prove that the solution of the involved neural networks exists and is unique and bounded. Second of all, we investigate the stability behavior and the onset of Hopf bifurcation of the involved network models by applying the stability theory and the related Hopf bifurcation knowledge on fractional-order differential equations. A suffi… Show more

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Cited by 29 publications
(21 citation statements)
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“…Among these results, one category has been mainly oriented toward analyses of the influence of (discrete) time delays on the dynamics of BAMNNs of differential equations with integer-order or fractional-order derivatives, as well as toward designing controls to reduce or even to remove complex dynamics such as bifurcation. Among the vast amount of existing studies, the references of [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] are most closely related to the topic discussed in this paper.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Among these results, one category has been mainly oriented toward analyses of the influence of (discrete) time delays on the dynamics of BAMNNs of differential equations with integer-order or fractional-order derivatives, as well as toward designing controls to reduce or even to remove complex dynamics such as bifurcation. Among the vast amount of existing studies, the references of [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] are most closely related to the topic discussed in this paper.…”
Section: Introductionmentioning
confidence: 99%
“…The DBAMNNs studied in [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] and the references therein can be written as…”
Section: Introductionmentioning
confidence: 99%
“…Hopf bifurcation driven by delay is an significant dynamical peculiarity in nonlinear delayed differential models [6][7][8][9][10][11][12][13][14][15][16]. In chemistry, Hopf bifurcation driven by delay can availably characterize the transformation relationship of the concentration of different chemical substances.…”
Section: Introductionmentioning
confidence: 99%
“…During the recent decades, numerous researchers hold that fractionalorder dynamical model can be considered a very valuable implement to depict the authentic natural law in object society than the integer-order ones because of the serious highlight of fractional-order dynamical model in the memory aspect and hereditary function of diverse substances and development process [21,22]. Recently, fractional-order dynamical model has aroused great interest from lots of researchers due to its tremendous application aspect in complex networks, life sciences, neural networks, electronics, mechanics, secure cryptography, finance, artificial intelligence, chemistry and so on [23][24][25][26][27][28]. Currently, abundant results on fractionalorder dynamical models have been acquired.…”
Section: Introductionmentioning
confidence: 99%