Impulsive synchronization of networked nonlinear dynamical systems

Jiang, Haibo; Bi, Qinsheng

doi:10.1016/j.physleta.2010.04.063

Cited by 67 publications

(38 citation statements)

References 32 publications

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“…For example, in [22][23][24], the impulsive control protocols have been introduced for networked linear and nonlinear dynamical systems. Blazejczyk-Okolewska et al [25] studied the dynamics of two mechanical oscillators coupled by impacts and observed the anti-phase synchronization phenomenon when the distance between these oscillators exceeded some critical thresholds.…”

Section: Introductionmentioning

confidence: 99%

Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators

Jiang

Liu

Zhang

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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This paper studies the synchronization in two mechanical oscillators coupled by impacts which can be considered as a class of state-dependent impulsively coupled oscillators. The two identical oscillators are harmonically excited in a counter phase, and the synchronous (antiphase synchronization) and the asynchronous motions are considered. One-and two-parameter bifurcations of the system have been studied by varying the amplitude and the frequency of external excitation. Numerical simulations show that the system could exhibit complex phenomena, including symmetry and asymmetry periodic solutions, quasi-periodic solutions and chaotic solutions. In particular, the regimes in anti-phase synchronization are identified, and it is found that the symmetry-breaking bifurcation plays an important role in the transition from synchronous to asynchronous motion.

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Section: Introductionmentioning

confidence: 99%

Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators

Jiang

Liu

Zhang

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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“…Interest in impulsive complex systems has grown in recent years and many effective, robust and inexpensive impulsive control strategies have been invented. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] Zhou et al, 16 for instance, investigated the synchronization of delayed dynamical networks with impulsive effects, and Yang and Chua 19 studied the impulsive stabilization problem for chaotic synchronization and control. Liu et al 20 considered robust impulsive synchronization of uncertain dynamical network.…”

Section: Introductionmentioning

confidence: 99%

“…The authors introduced impulsive control protocols for multi-agent linear continuous dynamic systems. 29,30 In the existing control schemes, some of the control strategies are based on the weighted average of the states of all nodes. This may lead to the difficulty, since it is not easy for a node to obtain information of all other nodes in a large scale network.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Han et al 35 proposed a model for impulsively coupled systems, i.e., systems that are coupled at discrete instants only via impulsive connections, and obtained sufficient conditions for their synchronization. However, in the existing works, in particularly, networked nonlinear dynamical systems coupled at certain discrete instants, 29,30,35 delays are not considered. Research shows that ignoring delays may lead to design flaws and incorrect analysis conclusions.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of impulsively coupled complex systems with delay

Sun

Austin

Lü

et al. 2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper investigates the synchronization of complex systems with delay that are impulsively coupled at discrete instants only. Based on the comparison theorem of impulsive differential system, a distributed impulsive control scheme is proposed to achieve the synchronization for systems with delay. In the control strategy, the influence of all nodes to network synchronization relies on its weight. The proposed control scheme is applied to the chaotic delayed Hopfield neural networks and numerical simulations are presented to demonstrate the effectiveness of the proposed scheme.

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“…On the other hand, networked dynamical systems can achieve synchronization without interacting with each other continuously. In [16,17], a kind of impulsive control protocol has been introduced for networked linear and nonlinear dynamical systems, respectively.…”

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confidence: 99%

Contraction theory based synchronization analysis of impulsively coupled oscillators

Jiang

2011

Nonlinear Dyn

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Impulsively coupled oscillators which are assumed to interact with each other only at discrete times have many applications in practice. In this paper, we introduce the concept of partial contraction theory of impulsive systems, which is used to investigate the synchronization problem of impulsively coupled oscillators. Contraction analysis of two impulsively coupled oscillators and networked impulsively coupled oscillators is provided, respectively. Very simple but very general results for synchronization of impulsively coupled oscillators are derived. Numerical simulations show the effectiveness of our theoretical results.

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Impulsive synchronization of networked nonlinear dynamical systems

Cited by 67 publications

References 32 publications

Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators

Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators

Synchronization of impulsively coupled complex systems with delay

Contraction theory based synchronization analysis of impulsively coupled oscillators

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