Probing into bifurcation for fractional-order BAM neural networks concerning multiple time delays

Xu, Changjin; Mu, Dan; Pan, Yuanlu; Aouiti, Chaouki; Pang, Yicheng; Yao, Lingyun

doi:10.1016/j.jocs.2022.101701

Cited by 18 publications

(22 citation statements)

References 52 publications

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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%

Bifurcation Analysis of Time-Delayed Non-Commensurate Caputo Fractional Bi-Directional Associative Memory Neural Networks Composed of Three Neurons

Wang,

Zhao,

Mai

et al. 2024

Fractal Fract

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We are concerned in this paper with the stability and bifurcation problems for three-neuron-based bi-directional associative memory neural networks that are involved with time delays in transmission terms and possess Caputo fractional derivatives of non-commensurate orders. For the fractional bi-directional associative memory neural networks that are dealt with in this paper, we view the time delays as the bifurcation parameters. Via a standard contraction mapping argument, we establish the existence and uniqueness of the state trajectories of the investigated fractional bi-directional associative memory neural networks. By utilizing the idea and technique of linearization, we analyze the influence of time delays on the dynamical behavior of the investigated neural networks, as well as establish and prove several stability/bifurcation criteria for the neural networks dealt with in this paper. According to each of our established criteria, the equilibrium states of the investigated fractional bi-directional associative memory neural networks are asymptotically stable when some of the time delays are less than strictly specific positive constants, i.e., when the thresholds or the bifurcation points undergo Hopf bifurcation in the concerned networks at the aforementioned threshold constants. In the meantime, we provide several illustrative examples to numerically and visually validate our stability and bifurcation results. Our stability and bifurcation theoretical results in this paper yield some insights into the cause mechanism of the bifurcation phenomena for some other complex phenomena, and this is extremely helpful for the design of feedback control to attenuate or even to remove such complex phenomena in the dynamics of fractional bi-directional associative memory neural networks with time delays.

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Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of Time-Delayed Non-Commensurate Caputo Fractional Bi-Directional Associative Memory Neural Networks Composed of Three Neurons

Wang,

Zhao,

Mai

et al. 2024

Fractal Fract

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“…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%

Exploration and Control of Bifurcation in a Fractional-Order Delayed Glycolytic Oscillator Model

Liu¹

2023

match

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Recently, establishing proper dynamical models to describe the relationship among different chemical substances has become a vital theme in chemistry. In this present article, we set up a new fractional-order delayed glycolytic oscillator model. Utilizing the contraction mapping theorem, we explore the existence and uniqueness of the solution to the involved fractional glycolytic oscillator model with delay. By virtue of some suitable analytical skills, we discuss the non-negativeness of the solution to the established fractional glycolytic oscillator system. Taking advantage of a suitable function, we investigate the boundedness of the fractional glycolytic oscillator system. Exploiting the stability and bifurcation theory of fractional dynamical system, we study the stability and the generation of Hopf bifurcation of the fractional glycolytic oscillator system with delay. Making use of delayed feedback controller and PDα controller, we deal with the Hopf bifurcation control of the fractional glycolytic oscillator system owing delay. Computer simulation results are displayed to support the obtained assertions. The acquired results of this article own great theoretical value in dominating the concentrations of different chemical compositions.

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“…In addition to the common stability [18][19][20][21], bifurcation [22][23][24], and periodicity [25], synchronization is also an important dynamic behavior and has gotten extensive attention [26][27][28][29][30][31][32][33][34][35][36][37]. Despite all this, there are not many articles about quasi-projective synchronization (QPS).…”

Section: Introductionmentioning

confidence: 99%

Laplace transform and nonlinear control design for quasi‐projective synchronization for Caputo inertial delayed neural networks

Zhang

Chen

et al. 2023

Math Methods in App Sciences

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The quasi‐projective synchronization problems for Caputo inertial neural networks (INNs) with delays are analyzed in this article. The considered model is transformed into two subsystems by selecting a suitable variable substitution. To realize synchronization, a novel fractional differential inequality is established, and the new lemma is derived via Laplace transform. Applying the given lemmas and inequality techniques, the synchronization conditions are inferred through different nonlinear feedback controllers. From the derivation of the theorems, it can be seen that the designed controllers are more extensive and efficacious. Furthermore, the error bound is validly estimated, and the validity of obtained theorems is illustrated by the numerical simulations.

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Probing into bifurcation for fractional-order BAM neural networks concerning multiple time delays

Cited by 18 publications

References 52 publications

Bifurcation Analysis of Time-Delayed Non-Commensurate Caputo Fractional Bi-Directional Associative Memory Neural Networks Composed of Three Neurons

Bifurcation Analysis of Time-Delayed Non-Commensurate Caputo Fractional Bi-Directional Associative Memory Neural Networks Composed of Three Neurons

Exploration and Control of Bifurcation in a Fractional-Order Delayed Glycolytic Oscillator Model

Laplace transform and nonlinear control design for quasi‐projective synchronization for Caputo inertial delayed neural networks

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