Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller

Yang, Xinsong; Cao, Jinde; Yang, Zhichun

doi:10.1137/120897341

Cited by 337 publications

(93 citation statements)

References 48 publications

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“…Therefore, increasing concerns have risen on the study of PDSs [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. A significant part of research is based on reaction-diffusion neural network models, such as [25,[34][35][36][37][38]. Multiple intercoupled reaction-diffusion neural networks can generate complex networks, as shown in the following example: the author of [25] discusses the passivity-based synchronization of a complex delayed dynamical network consisting of linearly 2 Complexity and diffusively coupled identical reaction-diffusion neural networks.…”

Section: Introductionmentioning

confidence: 99%

Exponential Synchronization of a Class of N-Coupled Complex Partial Differential Systems with Time-Varying Delay

et al. 2017

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This paper is concerned with the exponential synchronization for a class of -coupled complex partial differential systems (PDSs) with time-varying delay. The synchronization error dynamic of the PDSs is defined in the -dimensional spatial domain. To achieve synchronization, we added a linear feedback controller. A sufficient condition is derived to ensure the exponential synchronization of the proposed networks using the Lyapunov-Krasovskii stability approach and matrix inequality technology. The proposed system has broad applications. Two example applications are presented in the final section of this paper to verify the proposed theoretical result.

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Section: Introductionmentioning

confidence: 99%

Exponential Synchronization of a Class of N-Coupled Complex Partial Differential Systems with Time-Varying Delay

et al. 2017

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“…Finally, the use of differential geometric methods in the modeling and control of FitzHugh-Nagumo neuron dynamics has been studied in (Zhang et al 2007;Denham 2005). Other indicative results on synchronizing control of coupled neural oscillators can be found in Cao and Wan (2014), Cao et al (2013), Li and Cao (2014), Liu and Cao (2011), Shen and Cao (2011) and Yang et al (2013).…”

Section: Introductionmentioning

confidence: 99%

Robust synchronization of coupled neural oscillators using the derivative-free nonlinear Kalman Filter

Rigatos

2014

Cogn Neurodyn

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A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.

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“…On the other hand, because of switching phenomenon, frequency change, or other sudden noise, the states of nodes in many real-world dynamical networks are often subject to instantaneous perturbations and experience abrupt changes at certain instants, i.e., they exhibit impulsive effects [31][32][33][34][35][36][37][38][41][42][43][44]. Impulsive effects can also be found in many evolutionary processes and biological systems [31,32,41].…”

Section: Introductionmentioning

confidence: 99%

“…[41][42][43][44]. Recently, much progress has been made in the investigation of synchronization of impulsive dynamical networks [31][32][33][34][35][36][37][38][39][40][41][42][43][44]. For instance, stochastic synchronization was addressed for delayed dynamical networks with desynchronizing and synchronizing impulses in [31].…”

Section: Introductionmentioning

confidence: 99%

Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach

Cai

Jia

et al. 2016

Nonlinear Dyn

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In this paper, the problem of exponential cluster synchronization of general hybrid-coupled impulsive dynamical networks with internal delay and delayed coupling is investigated. A more general delayed coupling term including different transmission delay and self-feedback delay is taken into account. By using average impulsive interval approach and the analysis technique, some novel globally exponential cluster synchronization criteria are derived analytically. It is noted that the internal delay, transmission delay and self-feedback delay are all time-varying and can be different from each other, the inner connecting matrices are not demanded to be diagonal and the coupling matrices are not restricted to be symmetric or irreducible, more consistent with the realistic networks. Particularly, it is shown that the derived cluster synchronization criteria are simultaneously applicable for studying general delayed dynamical networks with

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Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller

Cited by 337 publications

References 48 publications

Exponential Synchronization of a Class of N-Coupled Complex Partial Differential Systems with Time-Varying Delay

Exponential Synchronization of a Class of N-Coupled Complex Partial Differential Systems with Time-Varying Delay

Robust synchronization of coupled neural oscillators using the derivative-free nonlinear Kalman Filter

Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach

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