Stability for a class of generalized reaction–diffusion uncertain stochastic neural networks with mixed delays

Lv, Tianshi; Gan, Qintao; Xiao, Feng

doi:10.1007/s13042-017-0775-4

Cited by 8 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…→ 0 as n → +∞. (12) By the Lebesgue dominated convergence theorem and (12), we can obtain thatÎ p 3 ,Î p 4 ,Î p 6 → 0 as n → +∞. From the estimates ofÎ…”

Section: Resultsmentioning

confidence: 88%

Almost Periodic Solutions in Distribution Sense for Quaternion-Valued Stochastic Delayed Neural Networks

Meng

2020

IEEE Access

View full text Add to dashboard Cite

In this paper, we consider quaternion-valued stochastic delayed neural networks. We first obtain the existence of almost periodic solutions in distribution sense by employing the contraction mapping principle. Then by using stochastic analysis and inequality techniques, we obtain the mean square global exponential stability of the almost periodic solutions of the considered neural networks. Finally, we present a numerical example to illustrate the feasibility of our results. INDEX TERMS Almost periodicity in distribution sense, mean square global exponential stability, quaternion-valued stochastic neural network.

show abstract

“…→ 0 as n → +∞. (12) By the Lebesgue dominated convergence theorem and (12), we can obtain thatÎ p 3 ,Î p 4 ,Î p 6 → 0 as n → +∞. From the estimates ofÎ…”

Section: Resultsmentioning

confidence: 88%

Almost Periodic Solutions in Distribution Sense for Quaternion-Valued Stochastic Delayed Neural Networks

Meng

2020

IEEE Access

View full text Add to dashboard Cite

show abstract

“…Mainly, semi-linear reaction-diffusion PDEs are commonly used to model a variety of real-world phenomenon such as population dynamics and chemical reactions etc., [31], [40]. Many researchers have focused their attention on reactiondiffusion equations due to their wide range of applications, see [1], [11], [12], [17], [25], [33]. Random noise in dynamical systems is caused by external disruptions, measurement errors, and a lack of knowledge of specific parameters.…”

Section: Introductionmentioning

confidence: 99%

Exponential Stability Analysis of Stochastic Semi-Linear Systems With Lèvy Noise

et al. 2022

View full text Add to dashboard Cite

The exponential stability of semi-linear stochastic partial differential equations (SPDEs) involving Lèvy type noise is investigated in this paper. By constructing an appropriate Lyapunov function, a new set of sufficient conditions are established in terms of linear matrix inequalities (LMIs) which ensures the mean-square exponentially stability (MSES) of given system with Neumann boundary conditions. Then the H ∞ performance index is introduced to eliminate the disturbance which occurs in the considered system. The boundary control gain is obtained by solving the LMI conditions using the standard MATLAB software. Finally, a numerical example is provided to demonstrate the usefulness of the proposed methods.

show abstract

Pointwise-Measurement-Based Event-Triggered Synchronization of Reaction-Diffusion Neural Networks

Zheng,

Song

2023

Communications in Computer and Information Science

View full text Add to dashboard Cite

Stability for a class of generalized reaction–diffusion uncertain stochastic neural networks with mixed delays

Cited by 8 publications

References 14 publications

Almost Periodic Solutions in Distribution Sense for Quaternion-Valued Stochastic Delayed Neural Networks

Almost Periodic Solutions in Distribution Sense for Quaternion-Valued Stochastic Delayed Neural Networks

Exponential Stability Analysis of Stochastic Semi-Linear Systems With Lèvy Noise

Pointwise-Measurement-Based Event-Triggered Synchronization of Reaction-Diffusion Neural Networks

Contact Info

Product

Resources

About