New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality

Xiao, Jianying; Wen, Shiping; Yang, Xujun; Zhong, Shouming

doi:10.1016/j.neunet.2019.10.017

Cited by 97 publications

(36 citation statements)

References 40 publications

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“…Recently, several activation functions been considered to study the QVNNs [32,33,38,40]. There are two different approaches that have been well regarded among them.…”

Section: Resultsmentioning

confidence: 99%

“…It is easy to know that the use of free-weighting parameters υ p (p = 1, ...12) can reduce the conservativeness of theoretical results. Thus, compared with that in [37,38,40], our approach is more effective and feasible.…”

Section: Theoremmentioning

confidence: 95%

“…In addition, fractional-order derivatives have many advantages compared to integer order calculus in defining an infinite memory and inherited properties [36]. Therefore, the use of fractional-order calculus in NN models could describe better dynamic behavior, and many excellent results on fractional-order NNs have been published, such as the problem of global robust synchronization, Mittag-Leffler synchronization, quasi-pinning synchronization, and finite-time Mittag-Leffler stability [37][38][39][40]. To the best of our knowledge, the current results of this paper have not yet been proposed for FOQVMNNs.…”

Section: Introductionmentioning

confidence: 99%

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Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

et al. 2020

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This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.

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“…Recently, several activation functions been considered to study the QVNNs [32,33,38,40]. There are two different approaches that have been well regarded among them.…”

Section: Resultsmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

et al. 2020

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“…In particular, the research on fractional-order neural networks has attracted widespread interest of many scholars. Numerous excellent fruits on fractional-order neural networks have been displayed (see previous studies [35][36][37][38] ).…”

Section: Introductionmentioning

confidence: 98%

Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Aouiti

2020

Circuit Theory & Apps

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Summary This article mainly focuses on the stability and the existence of Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay. First of all, we obtain the sufficient criterion to ensure the stability and the existence of Hopf bifurcation of integer‐order two‐neuron neural networks with delay. Next, we establish the sufficient condition guaranteeing the stability and the existence of Hopf bifurcation of fractional‐order two‐neuron neural networks with delay. The study reveals that the time delay has a vital effect on the stability and Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay. By comparative analysis on Hopf bifurcation for integer‐order and fractional‐order two‐neuron neural networks with delay, we find that under an appropriate parameter conditions, the stability region can be enlarged, and the time of appearance of Hopf bifurcation of the involved two‐neuron neural networks can be postponed by using fractional‐order case. Finally, computer simulation results are presented to illustrate the theoretical findings. The established results of this article play an important role in designing and controlling networks.

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“…Xiao et al. [73–74] studied new approach to global Mittag‐Leffler synchronization problem of fractional‐order seepage equation. Feng et al.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of oil‐water two‐phase flow for a multiple‐fractured horizontal well with multiple finite‐conductivity fractures in triple media carbonate reservoir

et al. 2020

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Carbonate reservoir is one of the important reservoir in the world. Because of the characteristics of carbonate reservoir, horizontal well and acid fracturing have become a key technology for efficiently developing carbonate reservoir. Establishing corresponding mathematical models and analyzing transient pressure behaviors of this type of well‐reservoir configuration can provide a better understanding of fluid flow patterns in formation as well as estimations of important parameters. A mathematical model for a oil‐water two‐phase flow multiple‐fractured horizontal well with multiple finite‐conductivity fractures in triple media carbonate reservoir by conceptualizing vugs as spherical shapes is presented in this article. A semi‐analytical solution is obtained in the Laplace domain by using source function theory, Laplace transformation, and superposition principle. Analysis of transient pressure responses indicates that nine characteristic flow periods of multiple‐fractured horizontal wells with multiple finite‐conductivity fractures in triple media carbonate reservoir can be identified. Parametric analysis shows that water saturation of matrix, vug and fracture system and acid fracture, fracture half‐length, fracture number, fracture spacing and acid fracture conductivity can significantly influence the transient pressure responses of multiple‐fractured horizontal wells with multiple finite‐conductivity fractures in triple media carbonate reservoir. The model presented in this article can be applied to obtain important parameters pertinent to reservoir or fracture by type curve matching, and it can also provide useful information for optimizing fracture parameters.

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New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality

Cited by 97 publications

References 40 publications

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Dynamic analysis of oil‐water two‐phase flow for a multiple‐fractured horizontal well with multiple finite‐conductivity fractures in triple media carbonate reservoir

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