Synchronization for complex networks with Markov switching via matrix measure approach

Pan, Lijun; Cao, Jinde; Hu, Jianqiang

doi:10.1016/j.apm.2015.01.027

Cited by 46 publications

(21 citation statements)

References 42 publications

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“…In [26] the mean square input-to-state stability was introduced to study neural networks. The technique is rather promising and might be particularly efficient in several important applied problems, for example, in the synchronization theory for networks with random switching [42].…”

Section: Resultsmentioning

confidence: 99%

Input-to-State Stability of Linear Stochastic Functional Differential Equations

Kadiev

Ponosov²

2016

Journal of Function Spaces

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The purpose of the paper is to show how asymptotic properties, first of all stochastic Lyapunov stability, of linear stochastic functional differential equations can be studied via the property of solvability of the equation in certain pairs of spaces of stochastic processes, the property which we call input-to-state stability with respect to these spaces. Input-to-state stability and hence the desired asymptotic properties can be effectively verified by means of a special regularization, also known as “theW-method” in the literature. How this framework provides verifiable conditions of different kinds of stochastic stability is shown.

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Section: Resultsmentioning

confidence: 99%

Input-to-State Stability of Linear Stochastic Functional Differential Equations

Kadiev

Ponosov²

2016

Journal of Function Spaces

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“…Synchronization of a complex network is a fascinating phenomena which is observed in fields such as physical, biological, chemical, technological, etc., and it has potential applications in biological systems, chemical reactions, secure communication, image processing and so on (Pan et al 2015;Cao 2014, 2012). Synchronization of coupled inertial neural networks means that multiple neural networks can achieve a common trajectory, such as a common equilibrium, limit cycle or chaotic trajectory.…”

Section: Introductionmentioning

confidence: 98%

Stability and synchronization analysis of inertial memristive neural networks with time delays

et al. 2016

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This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.

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“…Therefore coupled networks with Markovian switching can better describe telegraph noise, whereas deterministic systems or stochastic systems driven by Brownian motion mentioned above cannot explain it. Synchronization of coupled networks with Markovian switching has received extensive attention [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Synchronization of stochastic multiple weighted coupled networks with Markovian switching

2020

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We investigate the synchronization of stochastic multiple weighted coupled networks with Markovian switching (SMWCNMS). By designing an appropriate controller, we obtain several sufficient criteria ensuring the pth moment exponential synchronization and almost surely exponential synchronization for SMWCNMS based on graph theory. Moreover, we also investigate the pth moment asymptotical synchronization and almost surely asymptotical synchronization for SMWCNMS. Finally, we provide a numerical example to illustrate the availability of the proposed synchronization criteria.

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Synchronization for complex networks with Markov switching via matrix measure approach

Cited by 46 publications

References 42 publications

Input-to-State Stability of Linear Stochastic Functional Differential Equations

Input-to-State Stability of Linear Stochastic Functional Differential Equations

Stability and synchronization analysis of inertial memristive neural networks with time delays

Synchronization of stochastic multiple weighted coupled networks with Markovian switching

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