Pinning control of successive lag synchronization on a dynamical network with noise perturbation

Wang, Mengchen; Lu, Xiaowen; Qi, Yang; Ma, Zhongjun; Cheng, Jun; Li, Kezan

doi:10.1016/j.physa.2022.126899

Cited by 7 publications

(4 citation statements)

References 44 publications

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“…Remark In References 15,16,18, and 19, the coupling matrix must be lower triangular in order to realize the SLS, which means that there are only connections from given nodes to other ones with bigger numbers (see the example A in Figure 1). This constraint of particular topological structures is removed in network (1) by introducing a new coupling strategy

{\sum}_{j=1}^N{A}_{ij}\left[{\xi}_j\left(t-{\alpha}_{ij}\tau \right)-{\xi}_i\left(t-{\beta}_{ij}\tau \right)\right]

so that arbitrary network structure is allowable for the study of SLS (see the example B in Figure 1).…”

Section: The Stochastic Network and Preliminariesmentioning

confidence: 99%

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Successive lag synchronization of nonlinear stochastic networks with arbitrary structure via pinning control

Wang

et al. 2022

Intl J Robust & Nonlinear

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In this article, a new nonlinear stochastic network with arbitrary structure and noise is proposed for realizing the successive lag synchronization (SLS).Both the constant and adaptive pinning control laws are designed respectively to regulate the SLS to desired chaotic states, where the network structure can be directed, weighted, time-varying and even not strongly connected. Several sufficient conditions for guaranteeing the stochastic asymptotic stability of SLS are derived by means of the Lyapunov stability theory. First, we demonstrate that the pinned nodes can be fixed via 1-dimensional inequalities, which explicitly provide how many nodes and which nodes should be controlled. Besides, those connections from a node with a given number to other nodes with smaller numbers will lead to the increase of pinned nodes. Second, our results indicate that, in order to make the SLS stable the coupling strength must belong to a bounded interval for both the pinning control schemes. Finally, we conclude that strong noise perturbation will lead to the increase of pinned nodes and even break the SLS. The theoretical results are validated with different numerical examples by embedding the chaotic Chua's circuit to each node.

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{\sum}_{j=1}^N{A}_{ij}\left[{\xi}_j\left(t-{\alpha}_{ij}\tau \right)-{\xi}_i\left(t-{\beta}_{ij}\tau \right)\right]

so that arbitrary network structure is allowable for the study of SLS (see the example B in Figure 1).…”

Section: The Stochastic Network and Preliminariesmentioning

confidence: 99%

“…Recently, the stability and control schemes of SLS on dynamical networks with particular topological structures have been investigated 15‐19 . These structures demand a particular way of connections, that is, each connection between a pair of nodes always points from the one with smaller number.…”

Section: Introductionmentioning

confidence: 99%

Successive lag synchronization of nonlinear stochastic networks with arbitrary structure via pinning control

Wang

et al. 2022

Intl J Robust & Nonlinear

Self Cite

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“…Synchronization is one of the important tools to study dynamical behavior. Recently, scholars have explored various types of synchronization and made some achievements, such as lag synchronization [18,29], finite-time synchronization [17], Mittag-Leffler synchronization [21,23], projective synchronization [4,14], and so on. Among them, lag projective synchronization has important research significance in practical applications.…”

Section: Introductionmentioning

confidence: 99%

Finite-time lag projective synchronization of delayed fractional-order quaternion-valued neural networks with parameter uncertainties

Shang

Zhang

et al. 2023

NAMC

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This paper discusses a class issue of finite-time lag projective synchronization (FTLPS) of delayed fractional-order quaternion-valued neural networks (FOQVNNs) with parameter uncertainties, which is solved by a non-decomposition method. Firstly, a new delayed FOQVNNs model with uncertain parameters is designed. Secondly, two types of feedback controller and adaptive controller without sign functions are designed in the quaternion domain. Based on the Lyapunov analysis method, the non-decomposition method is applied to replace the decomposition method that requires complex calculations, combined with some quaternion inequality techniques, to accurately estimate the settling time of FTLPS. Finally, the correctness of the obtained theoretical results is testified by a numerical simulation example.

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“…Al-Mahbashi et al [14] studied the lag synchronization of complex networks with disturbances via adaptive control. Wang et al [15] studied the lag synchronization of complex networks with noise via pinning control. Furthermore, convergence may be slow during network synchronization.…”

Section: Introductionmentioning

confidence: 99%

Lag exponential synchronization of fractional-order complex-valued dynamical networks with multiple delays via adaptive control

Ding

Wang

et al. 2022

Preprint

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In this paper, the lag exponential synchronization issue of fractional-order complex-valued dynamic networks with multiple delays is studied. Considering the uncertain factors in the networks, a system model with uncertain disturbance and coupling strength is established. In addition, in order to study the dynamic behavior of complex networks under different coupling delays, symmetric and un symmetric matrices are used to model the coupling systems, respectively. By using Lyapunov stability theorem and fractional-order theory, the criterion of lag exponential synchronization of complex networks via adaptive control are obtained. The result extends the single delay problem of fractional-order complex-valued systems to multiple delays. Finally, two examples of fractional-order complex-valued systems are given to verify the correctness of the theoretical derivation.

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Pinning control of successive lag synchronization on a dynamical network with noise perturbation

Cited by 7 publications

References 44 publications

Successive lag synchronization of nonlinear stochastic networks with arbitrary structure via pinning control

Successive lag synchronization of nonlinear stochastic networks with arbitrary structure via pinning control

Finite-time lag projective synchronization of delayed fractional-order quaternion-valued neural networks with parameter uncertainties

Lag exponential synchronization of fractional-order complex-valued dynamical networks with multiple delays via adaptive control

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