【作者】 陈姚； 吕金虎；

【Author】 Yao Chen1,Jinhu Lv1 1Academy of Mathematics and Systems Science,Beijing 100190,China

【机构】 中科院数学与系统科学研究院；

【摘要】 复杂网络的同步问题是复杂网络研究中的一个非常重要的方向,许多学者从不同的角度对同步问题进行了深入的研究,比如:簇同步,部分结点同步等等。已有的结果中刻画同步的速度往往是渐进的,只有当时间趋于无穷的时候,结点状态间的差才会趋于零,而对于网络在多长时间内可以实现同步却知之甚少。为使复杂网络中各个结点的动力学趋于一致,通常需要引入扩散线性耦合。然而,由于非线性所具有的某些特殊属性,非线性耦合可以起到改善同步品质的作用。本文在复杂网络中引入一类非线性的耦合,证明了在满足某种条件的情况下,各个节点的动力学可以在有限时间内实现精确的同步。从而避免了各个结点状态只有在无穷时刻时才会相等的问题。更多还原

【Abstract】 The synchronization problem of complex networks has been an important direction in the fields of complex networks research;many results have been gained from different aspects,such as cluster synchronization and partial synchronization.However,among these results,the error between nodes dynamics converge to zero asymptotically,it is unknown that how much time is needed to reach synchronization accurately.Usually,to make the nodes states synchronize,diffusive and linear coupling is introduced.For the special property of nonlinearity,nonlinear coupling can improve the quality of synchronization.In this paper,a kind of nonlinear coupling is introduced and results show that under some conditions,the error between nodes states can reach zero accurately within finite-time.Hence,the problem that the synchronization time is unknown has been avoided.更多还原