Existence, uniqueness and stability of mild solutions to stochastic reaction–diffusion Cohen–Grossberg neural networks with delays and Wiener processes

Wei, Tengda; Wang, Linshan; Wang, Yangfan

doi:10.1016/j.neucom.2017.01.069

Cited by 20 publications

(14 citation statements)

References 33 publications

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“…then system (1) achieves asymptotic mean square stability under the boundary controller (4). In addition, the control gain is given by Take V(y(⋅, t), i) as (6). From the proof of Theorem 1, we know that…”

Section: Boundary Stabilization With Partially Unknown Transition Promentioning

confidence: 97%

“…Proof. Defining the same Lyapunov functional as (6), and computing dV along the system trajectory yields…”

Section: H-infinity Boundary Control For Smrdssmentioning

confidence: 99%

“…In recent years, the study of stochastic reaction-diffusion systems (SRDSs) has taken on an upsurge, and fruitful results of dynamical properties for SRDSs have been reported. [4][5][6] Especially there has been increasing interest in the topic of asymptotic stability properties. For more details, one can refer to References 7-9 and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Boundary control of stochastic reaction‐diffusion systems with Markovian switching

Han

Ding

et al. 2020

Intl J Robust & Nonlinear

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This article focuses on the boundary control of stochastic Markovian reaction-diffusion systems (SMRDSs). Both the cases of completely known and partially unknown transition probabilities are taken into account. By using the Lyapunov functional method, a sufficient condition is obtained under the designed boundary controllers to guarantee the asymptotic mean square stability for SMRDSs with completely known transition probabilities. For the case of partially unknown transition probabilities, we introduce free-connection weighting matrices to handle the boundary control problem. When external disturbance enters the system, a sufficient criterion of H-infinity boundary control is developed. Furthermore, robust stabilization is investigated for parametric uncertain SMRDSs in both cases. Two examples are presented to demonstrate the efficiency of the proposed approaches. K E Y W O R D S asymptotic stability, boundary control, H-infinity control, partially unknown transition probabilities, stochastic Markovian reaction-diffusion systems Int J Robust Nonlinear Control. 2020;30:4129-4148.wileyonlinelibrary.com/journal/rnc

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Section: Boundary Stabilization With Partially Unknown Transition Promentioning

confidence: 97%

“…Proof. Defining the same Lyapunov functional as (6), and computing dV along the system trajectory yields…”

Section: H-infinity Boundary Control For Smrdssmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Boundary control of stochastic reaction‐diffusion systems with Markovian switching

Han

Ding

et al. 2020

Intl J Robust & Nonlinear

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“…For instance, the interactions arising from the space-distributed structure of the multilayer cellular neural networks can be seen as diffusion phenomenon [24]. Hence, stochastic impulsive reaction-diffusion neural networks (SIRDNNs) have attracted much attention of researchers [29,35,40]. On the other hand, the time delay often occurs in the electronic implementation of analog networks because of the finite speed of signal transmission and amplifier switching.…”

Section: Introductionmentioning

confidence: 99%

“…From Lemma 6, we see that system(19) is globally exponentially stable in the mean-square sense, if 0 < γ < 1 and (20) hold. In this paper, we establish the stability conditions of SIRDNNs with Stype distributed delays while Refs [35,40]. does not consider the distributed delays.…”

mentioning

confidence: 99%

Stability of stochastic impulsive reaction–diffusion neural networks with S-type distributed delays and its application to image encryption

et al. 2019

Self Cite

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In this paper, we study stochastic impulsive reaction-diffusion neural networks with S-type distributed delays, aiming to obtain the sufficient conditions for global exponential stability. First, an impulsive inequality involving infinite delay is introduced and the asymptotic behaviour of its solution is investigated by the truncation method. Then, global exponential stability in the mean-square sense of the stochastic impulsive reaction-diffusion system is studied by constructing a simple Lyapunov-Krasovskii functional where the S-type distributed delay is handled by the impulsive inequality. Numerical examples are also given to verify the effectiveness of the proposed results. Finally, the obtained theoretical results are successfully applied to an image encryption scheme based on bit-level permutation and the stochastic neural networks.

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Adaptive synchronization of stochastic complex dynamical networks and its application

Wei

Yao

Lin

et al. 2018

Neural Comput & Applic

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This paper investigates exponential synchronization for stochastic complex dynamical networks with reaction-diffusion terms and S-type distributed delays. Based on a generalized Halanay inequality and Poincaré inequality, adaptive control strategies for exponential synchronization are established by constructing a simple Lyapunov-Krasovskii functional candidate and utilizing the truncation method. Some numerical examples are provided to demonstrate the effectiveness of the obtained results. Finally, the proposed adaptive synchronization theoretical results are successfully applied to image encryption.

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Existence, uniqueness and stability of mild solutions to stochastic reaction–diffusion Cohen–Grossberg neural networks with delays and Wiener processes

Cited by 20 publications

References 33 publications

Boundary control of stochastic reaction‐diffusion systems with Markovian switching

Boundary control of stochastic reaction‐diffusion systems with Markovian switching

Stability of stochastic impulsive reaction–diffusion neural networks with S-type distributed delays and its application to image encryption

Adaptive synchronization of stochastic complex dynamical networks and its application

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