Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations.A community network with distributed time delays is investigated in this paper.For achieving cluster...Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations.A community network with distributed time delays is investigated in this paper.For achieving cluster synchronization,an impulsive control scheme is introduced to design proper controllers and an adaptive strategy is adopted to make the impulsive controllers unified for different networks.Through taking advantage of the linear matrix inequality technique and constructing Lyapunov functions,some synchronization criteria with respect to the impulsive gains,instants,and system parameters without adaptive strategy are obtained and generalized to the adaptive case.Finally,numerical examples are presented to demonstrate the effectiveness of the theoretical results.展开更多
Abstract Generalized B-splines have been employed as geometric modeling and numerical simu- lation tools for isogeometric analysis （IGA for short）. However, the previous models used in IGA, such as trigonometric gen...Abstract Generalized B-splines have been employed as geometric modeling and numerical simu- lation tools for isogeometric analysis （IGA for short）. However, the previous models used in IGA, such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper, a unified approach to construct the generalized non-uniform B-splines over the space spanned by {α（t）,β（t）,ξ（t）, η（t）, 1, t,……. , tn-4} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometrie heat conduction problems are presented to show the effectiveness of the proposed methods.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61463022)the Natural Science Foundation of Jiangxi Province,China(Grant No.20161BAB201021)the Natural Science Foundation of Jiangxi Educational Committee,China(Grant No.GJJ14273)
文摘Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations.A community network with distributed time delays is investigated in this paper.For achieving cluster synchronization,an impulsive control scheme is introduced to design proper controllers and an adaptive strategy is adopted to make the impulsive controllers unified for different networks.Through taking advantage of the linear matrix inequality technique and constructing Lyapunov functions,some synchronization criteria with respect to the impulsive gains,instants,and system parameters without adaptive strategy are obtained and generalized to the adaptive case.Finally,numerical examples are presented to demonstrate the effectiveness of the theoretical results.
基金supported by Zhejiang Provincial Natural Science Foundation of China under Grant No.LR16F020003the National Nature Science Foundation of China under Grant Nos.61472111,61602138+1 种基金the Open Project Program of the State Key Lab of CAD&CG(A1703)Zhejiang University
文摘Abstract Generalized B-splines have been employed as geometric modeling and numerical simu- lation tools for isogeometric analysis （IGA for short）. However, the previous models used in IGA, such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper, a unified approach to construct the generalized non-uniform B-splines over the space spanned by {α（t）,β（t）,ξ（t）, η（t）, 1, t,……. , tn-4} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometrie heat conduction problems are presented to show the effectiveness of the proposed methods.
