Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory

Zhang, Chunmei; Han, Byungjin

doi:10.1016/j.physa.2019.122827

Cited by 51 publications

(23 citation statements)

References 41 publications

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“…In recent years, constructing a Lyapunov function by digraph theory has attracted much attention, and many interesting results have been obtained. [44][45][46][47] In B1. There are positive constants A (i) q such that…”

Section: Combining L Amentioning

confidence: 99%

Exponential bipartite synchronization of random signed networks with Markovian switching via impulsive control

Wang

Xie

2020

Intl J Robust & Nonlinear

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In this article, exponential bipartite synchronization in mth moment of random signed networks is studied. Different from previous work, both random disturbances and Markovian switching are considered into signed networks. It is worth emphasizing that the topological structure of signed networks depends on Markovian switching, and not all switching subnetworks are required to be strongly connected. In addition, an impulsive controller is designed to make random signed networks with Markovian switching achieve bipartite synchronization. Then, by using Lyapunov method and signed digraph theory, two synchronization criteria are obtained. These criteria have a close relationship with the topological structure of signed networks, the impulsive gain and the reverse average impulsive interval. Furthermore, our theoretical results are applied to studying exponential bipartite synchronization in mth moment of single-link robot arms in engineering, and a synchronization criterion is given. Finally, some numerical simulations are shown to illustrate the effectiveness and feasibility of theoretical results.

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Section: Combining L Amentioning

confidence: 99%

Exponential bipartite synchronization of random signed networks with Markovian switching via impulsive control

Wang

Xie

2020

Intl J Robust & Nonlinear

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“…Remark 3 The related results in the literature are divided into two parts: one is mainly about the synchronization of complex networks with multiple weights but without stochastic perturbations [31][32][33][34]36], whereas the other part is about the synchronization of stochastic complex networks with single weight [12,26]. Only few papers investigated the synchronization of stochastic multiple complex networks with white noise or Lévy noise [22,29,35,46]. We focus on the synchronization of stochastic multiple complex networks with white noise and telegraph noise.…”

Section: Synchronization Analysis For Drive-response Network (1) Andmentioning

confidence: 99%

“…In the multi-weighted networks, different weights have different properties. Hence they cannot simply merge into a single-weighted network [28,29]. For instance, in the social network, people can communicate with others by multiple ways, such as mobile phone, Wechat, E-mail, and so on.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of stochastic multiple weighted coupled networks with Markovian switching

2020

Self Cite

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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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“…[4][5][6] In particular, synchronization is a collective typical behavior in dynamical network, which not only can explain many natural phenomena, such as the spread of an epidemic and the lighting of fireflies, but also has extensive applications, including image processing and secure communication, see Wang. 7 Thus, synchronization for SCN has been a hot topic in the past few years, and numerous related results have been carried out (see the works of other studies [8][9][10][11] ). For example, Li et al 10 studied the synchronization of stochastic hybrid coupled systems with multi-weights and mixed delays.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Li et al 10 studied the synchronization of stochastic hybrid coupled systems with multi-weights and mixed delays. Moreover, time delays, which may affect dynamic behaviors, are inevitably encountered in many practical systems, [10][11][12][13] and it is therefore reasonable and necessary to investigate synchronization for stochastic-delayed coupled systems on networks (SDCN).…”

Section: Introductionmentioning

confidence: 99%

Synchronization for stochastic hybrid coupled controlled systems with Lévy noise

Zhou

2020

Math Methods in App Sciences

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In this paper, synchronization for stochastic hybrid-delayed coupled systems with Lévy noise on a network (SHDCLN) is investigated via aperiodically intermittent control. Here time delays, Markovian switching and Lévy noise are considered on a network simultaneously for the first time. After that, by means of Lyapunov method, graph theory, and some techniques of inequality, some sufficient conditions are derived to guarantee the synchronization for SHDCLN. In addition, the designed range of aperiodically intermittent controller parameters is shown. Meanwhile, the coupling strength and the perturbed intensity of noise have a great impact on the intensity of control. Then, we investigate synchronization for stochastic hybrid delayed Chua's circuits with Lévy noise on a network as a practical application of our theoretical results. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

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Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory

Cited by 51 publications

References 41 publications

Exponential bipartite synchronization of random signed networks with Markovian switching via impulsive control

Exponential bipartite synchronization of random signed networks with Markovian switching via impulsive control

Synchronization of stochastic multiple weighted coupled networks with Markovian switching

Synchronization for stochastic hybrid coupled controlled systems with Lévy noise

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