In the paper, we study effects of scale-free （SF） topology on dynamical synchronization and control in coupled map lattices （CIVIL）. Our strategy is to apply three feedback control methods, including constant feed...In the paper, we study effects of scale-free （SF） topology on dynamical synchronization and control in coupled map lattices （CIVIL）. Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength γc for the first time-delayed feedback control is increased linearly as e is increased linearly. The GML with SF loses synchronization and intermittency occurs if γ 〉 γc. Numerical examples are presented to demonstrate all results.展开更多
The effective theory for the hierarchical fractional quantum Hall (FQH) effect is proposed. We also derive the topological numbers K matrix and t vector and the general edge excitation from the effective theory. One c...The effective theory for the hierarchical fractional quantum Hall (FQH) effect is proposed. We also derive the topological numbers K matrix and t vector and the general edge excitation from the effective theory. One can End that the two issues in rapidly rotating ultracold atoms are similar to those in electron FQH liquid.展开更多
基金The project supported by the Key Program of National Natural Science Foundation of China under Grant No. 70431002 and National Natural Science Foundation of China under Grant Nos. 70371068 and 10247005 The authors thank Drs. Atay and Chun-Guang Li for their useful advices and discussions.
文摘In the paper, we study effects of scale-free （SF） topology on dynamical synchronization and control in coupled map lattices （CIVIL）. Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength γc for the first time-delayed feedback control is increased linearly as e is increased linearly. The GML with SF loses synchronization and intermittency occurs if γ 〉 γc. Numerical examples are presented to demonstrate all results.
文摘The effective theory for the hierarchical fractional quantum Hall (FQH) effect is proposed. We also derive the topological numbers K matrix and t vector and the general edge excitation from the effective theory. One can End that the two issues in rapidly rotating ultracold atoms are similar to those in electron FQH liquid.
