Adaptive Output Synchronization of General Complex Dynamical Network with Time-Varying Delays

Gan, Li; Li, Shuo; Duan, Na; Kong, Xiangyong

doi:10.3390/math8030311

Cited by 4 publications

(2 citation statements)

References 32 publications

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“…It is well known that various time delays are unavoidable in actual engineering applications. The time delay may destroy the dynamic characteristics and decrease the stability of the system, which is extremely detrimental to the control system [17][18][19]. Multiple time-varying delay couplings mean that multiple different time-varying delays exist in the complex network.…”

Section: Introductionmentioning

confidence: 99%

Function Projective Synchronization of Two Complex Networks with Unknown Sector Nonlinear Input and Multiple Time-Varying Delay Couplings

Fang

Wei

Yin

et al. 2022

Advances in Mathematical Physics

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This paper deals with the function projective synchronization of two complex dynamic networks with unknown sector nonlinear input, multiple time-varying delay couplings, model uncertainty, and external interferences. Based on Lyapunov stability theory and inequality transformation method, the robust adaptive synchronization controller is designed, by which the drive and response systems can achieve synchronization according to the function scaling factor. Different from some existing studies on nonlinear system with sector nonlinear input, this paper studies the synchronization of two complex dynamic networks when the boundary of sector nonlinear input is unknown. The controller does not include the boundary value of the sector nonlinear input and the time delay term, so it is more practical and relatively easy to implement. The corresponding simulation examples demonstrate the effectiveness of the proposed scheme.

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Section: Introductionmentioning

confidence: 99%

Function Projective Synchronization of Two Complex Networks with Unknown Sector Nonlinear Input and Multiple Time-Varying Delay Couplings

Fang

Wei

Yin

et al. 2022

Advances in Mathematical Physics

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“…Changes along time refer to changes in the couplings between nodes which are defined as function purely of time. In this sense, the changes in the network are dictated by an external agent, and the nodes in the networks do not influence their couplings, for instance in Reference [17] the authors consider varying couplings but a control action is implemented to achieve synchronization in a defined reference. Another example is in brain deceases or disorders such as Parkinson, Alzheimer's, and so forth, where external deep brain stimulation is provided to modify the behavior of certain parts of the brain [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Synchronization in Time-Varying and Evolving Complex Networks

2020

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In this contribution, we present the synchronization in dynamical complex networks with varying couplings. We identify two kinds of variations—(i) Non autonomous (Time-varying) couplings: where the coupling strength depends exclusively on time, (ii) Autonomous or Varying couplings (evolution) where the coupling strength depends on the behavior of the interconnected systems. The coupling strength in (i) is exogenous whereas in (ii) the coupling strength is endogenous and is defined by the states of the systems in the nodes. The exponential stability of the synchronization is ensured for the non autonomous couplings, due to the imposition of the coupling strength. Whereas, in the case of evolutionary couplings the exponential stability of the synchronization is not guaranteed for all time, due to the couplings are not controlled or imposed. We present an overview of these features in complex networks and illustrated by means of numerical examples.

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Embeddedness of min–max CMC hypersurfaces in manifolds with positive Ricci curvature

Bellettini,

Workman

2024

Nonlinear Differ. Equ. Appl.

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We prove that on a compact Riemannian manifold of dimension 3 or higher, with positive Ricci curvature, the Allen–Cahn min–max scheme in Bellettini and Wickramasekera (The Inhomogeneous Allen–Cahn Equation and the Existence of Prescribed-Mean-Curvature Hypersurfaces, 2020), with prescribing function taken to be a non-zero constant $$\lambda $$ λ , produces an embedded hypersurface of constant mean curvature $$\lambda $$ λ ($$\lambda $$ λ -CMC). More precisely, we prove that the interface arising from said min–max contains no even-multiplicity minimal hypersurface and no quasi-embedded points (both of these occurrences are in principle possible in the conclusions of Bellettini and Wickramasekera, 2020). The immediate geometric corollary is the existence (in ambient manifolds as above) of embedded, closed $$\lambda $$ λ -CMC hypersurfaces (with Morse index 1) for any prescribed non-zero constant $$\lambda $$ λ , with the expected singular set when the ambient dimension is 8 or higher.

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Adaptive Output Synchronization of General Complex Dynamical Network with Time-Varying Delays

Cited by 4 publications

References 32 publications

Function Projective Synchronization of Two Complex Networks with Unknown Sector Nonlinear Input and Multiple Time-Varying Delay Couplings

Function Projective Synchronization of Two Complex Networks with Unknown Sector Nonlinear Input and Multiple Time-Varying Delay Couplings

Synchronization in Time-Varying and Evolving Complex Networks

Embeddedness of min–max CMC hypersurfaces in manifolds with positive Ricci curvature

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