Synchronization and stability of delayed fractional-order memristive quaternion-valued neural networks with parameter uncertainties

Xiao, Jianying; Zhong, Shouming

doi:10.1016/j.neucom.2019.06.044

Cited by 58 publications

(16 citation statements)

References 43 publications

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“…In practice, the main advantage of using quaternion is that it can view and operate three-dimensional or four-dimensional vectors as a single entity that significantly reduces computational complexity in multidimensional problems and by employing quaternion variables can achieve efficient information processing directly [23][24][25]. Therefore, QVNNs have been successfully implemented in body images, attitude control of satellites, computer graphics, 3D wind forecasting, 4D signals, color-face recognition, and vector sensor processing [26][27][28][29][30][31][32][33]. The problem of global µ stability for QVNNs with mixed time delays was studied in [22].…”

Section: Introductionmentioning

confidence: 99%

“…In [27], leakage delay-dependent synchronization conditions for fractional-order QVNNs with discrete delays have been studied. Based on the parameter uncertainties, sufficient conditions are obtained for stability and synchronization of fractional-order memristive QVNNs [30]. The problem of global Mittag-Leffler stability and synchronization for fractional-order QVNNs was studied in [31].…”

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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…It has a tremendous potential to be utilized in synapsis for simulation of the human brain by replacing a resistor with a memristor [4][5][6]. In view of these characteristics, a new neural network (NN) model, namely, the memristive neural network (MNN) has been widely studied, and many theoretical papers regarding various dynamics of MNNs have been published in recent years [7][8][9][10][11][12][13]. From the real-world application perspective, time delays inherently arise in many practical systems including NNs.…”

Section: Introductionmentioning

confidence: 99%

“…Undoubtedly, quaternion-based networks present good mathematical models to undertake these applications due to the quaternion features. In view of this, quaternion-valued neural networks (QVNNs) have been developed by implementing quaternion algebra into CVNNs, in order to generalize RVNN and CVNN models with quaternion-valued activation functions, connection weights, as well as signals states [11,[29][30][31][32]. Therefore, the investigation of the dynamics of QVNN models is essential and important.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability

et al. 2020

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In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying It o ^ ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.

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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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Synchronization and stability of delayed fractional-order memristive quaternion-valued neural networks with parameter uncertainties

Cited by 58 publications

References 43 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

Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability

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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