The stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms

Tan, Jie; Li, Chuandong; Huang, Tingwen

doi:10.1007/s11571-014-9316-y

Cited by 13 publications

(3 citation statements)

References 36 publications

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“…Remark 3.3. The impulsive control approach was utilized to stabilize the RDSs [37][38][39]49] and the boundary control technique was also utilized to stabilize the RDSs [9,15,16,22,23,51,52]. To best of our knowledge, there are few works that investigate the FTS and stabilization of SNIRDSs with time delays and the boundary feedback control.…”

Section: Theorem 32 Let T Be the Average Impulsive Interval Ofmentioning

confidence: 99%

Impulsive effects on stabilization of stochastic nonlinear reaction-diffusion systems with time delays and boundary feedback control

Gokulakrishnan¹,

Srinivasan²

2022

J. Math. Computer Sci.

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In this paper, we investigate the stabilization of stochastic nonlinear impulsive reaction-diffusion systems (SNIRDSs) with time delays and boundary feedback control via average impulsive interval approach. Boundary feedback control strategy are designed to stabilization of SNIRDSs. By constructing a Lyapunov-Krasovskii functional (LKF), and using Wirtinger's inequality, Gronwall inequality, average impulsive interval approach, sufficient conditions are derived to guarantee the finite-time stability (FTS) of proposed systems. We investigate the stabilization results by designing the control gain matrices for boundary feedback controller. The criterions are expressed in terms of linear matrix inequalities (LMIs) that can be verified by Matlab LMI toolbox. Finally, numerical example are given to verify the efficiency and superiority of proposed stabilization criterions.

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Section: Theorem 32 Let T Be the Average Impulsive Interval Ofmentioning

confidence: 99%

Impulsive effects on stabilization of stochastic nonlinear reaction-diffusion systems with time delays and boundary feedback control

Gokulakrishnan¹,

Srinivasan²

2022

J. Math. Computer Sci.

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“…Thus, it is necessary to implement discrete-time controllers. The impulsive controllers (Yang 2001;Lu et al 2013Lu et al , 2010Tan et al 2015;Qi et al 2014;Pu et al 2015) and the sampled data controllers (Chen and Francis 1995;Yu et al 2013bYu et al , 2011a are two typical types of controllers with discrete time updates. In Å ström and Bernhardsson (2002) andÅ ström (2008), the authors proposed the event-triggered controllers.…”

Section: Introductionmentioning

confidence: 99%

Event-based exponential synchronization of complex networks

2016

Self Cite

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In this paper, we consider exponential synchronization of complex networks. The information diffusions between nodes are driven by properly defined events. By employing the M-matrix theory, algebraic graph theory and the Lyapunov method, two kinds of distributed eventtriggering laws are designed, which avoid continuous communications between nodes. Then, several criteria that ensure the event-based exponential synchronization are presented, and the exponential convergence rates are obtained as well. Furthermore, we prove that Zeno behavior of the event-triggering laws can be excluded before synchronization being achieved, that is, the lower bounds of inter-event times are strictly positive. Finally, a simulation example is provided to illustrate the effectiveness of theoretical analysis.

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“…Neural networks have attracted much attention due to their applications in many areas of real world problems such as optimization problems, associative memory, classification of patterns etc., So far, there are various types of neural networks such as cellular neural networks (CNNs), bidirectional associative memory neural networks (BAMNNs), Hopfield neural network (HNNs), Chaotic neural networks and Cohen-Grossberg neural network (CGNNs) which have been studied by many researchers for their enormous applications, see (Cao and Wang 2003;Cho and Park 2007;Haykin 1999;Kosko 1992;Liu 1997;Meng and Wang 2007;Mou et al 2008;Senan and Arik 2007;Tan et al 2015;Wang et al 2008;Yang et al 2014). These applications heavily depend on the stability of the equilibrium point of neural networks.…”

Section: Introductionmentioning

confidence: 99%

New stability criterion of neural networks with leakage delays and impulses: a piecewise delay method

Kumar

Sugumaran²,

Raja

et al. 2015

Cogn Neurodyn

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This paper analyzes the global asymptotic stability of a class of neural networks with time delay in the leakage term and time-varying delays under impulsive perturbations. Here the time-varying delays are assumed to be piecewise. In this method, the interval of the variation is divided into two subintervals by its central point. By developing a new Lyapunov-Krasovskii functional and checking its variation in between the two subintervals, respectively, and then we present some sufficient conditions to guarantee the global asymptotic stability of the equilibrium point for the considered neural network. The proposed results which do not require the boundedness, differentiability and monotonicity of the activation functions, can be easily verified via the linear matrix inequality (LMI) control toolbox in MATLAB. Finally, a numerical example and its simulation are given to show the conditions obtained are new and less conservative than some existing ones in the literature.

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The stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms

Cited by 13 publications

References 36 publications

Impulsive effects on stabilization of stochastic nonlinear reaction-diffusion systems with time delays and boundary feedback control

Impulsive effects on stabilization of stochastic nonlinear reaction-diffusion systems with time delays and boundary feedback control

Event-based exponential synchronization of complex networks

New stability criterion of neural networks with leakage delays and impulses: a piecewise delay method

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