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
In this paper,we study precise large deviation for the non-random difference sum from j=1 to n1（t） X1j-sum from j=1 to n2（t） X2j,where sum from j=1 to n1（t） X1j is the non-random sum of {X1j,j≥1} which is a seq...In this paper,we study precise large deviation for the non-random difference sum from j=1 to n1（t） X1j-sum from j=1 to n2（t） X2j,where sum from j=1 to n1（t） X1j is the non-random sum of {X1j,j≥1} which is a sequence of negatively associated random variables with common distribution F1（x）,and sum from j=1 to n2（t） X2j is the non-random sum of {X2j,j≥1} which is a sequence of independent and identically distributed random variables,n1（t） and n2（t） are two positive integer functions.Under some other mild conditions,we establish the following uniformly asymptotic relation lim t→∞ sup x≥r（n1（t））p＋1｜（P（∑（n1（t）j=1）X1j-∑n2（t）（j=1）X（2j）-（μ1n1（t）-μ2n2（t）〉x））/（n1（t）F1（x））-1｜=0.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 the National Natural Science Foundation of China(Grant Nos.1137107711571058)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.DUT15LK19)the Natural Science Foundation of Inner Mongolia University for the Nationalities(Grant Nos.NMDYB1436NMDYB1437)
文摘In this paper,we study precise large deviation for the non-random difference sum from j=1 to n1（t） X1j-sum from j=1 to n2（t） X2j,where sum from j=1 to n1（t） X1j is the non-random sum of {X1j,j≥1} which is a sequence of negatively associated random variables with common distribution F1（x）,and sum from j=1 to n2（t） X2j is the non-random sum of {X2j,j≥1} which is a sequence of independent and identically distributed random variables,n1（t） and n2（t） are two positive integer functions.Under some other mild conditions,we establish the following uniformly asymptotic relation lim t→∞ sup x≥r（n1（t））p＋1｜（P（∑（n1（t）j=1）X1j-∑n2（t）（j=1）X（2j）-（μ1n1（t）-μ2n2（t）〉x））/（n1（t）F1（x））-1｜=0.
