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
This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, ...This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, the definition of decomposition w.r.t. outputs is introduced. Second, by referring to the graphical structure of BCNs, a necessary and sufficient condition for the decomposition w.r.t. outputs is obtained based on graph theory method. Third, an effective algorithm to realize the maximum decomposition w.r.t. outputs is proposed. Finally, some examples are addressed to validate the theoretical results.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.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.61673012,11271194a Project on the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, the definition of decomposition w.r.t. outputs is introduced. Second, by referring to the graphical structure of BCNs, a necessary and sufficient condition for the decomposition w.r.t. outputs is obtained based on graph theory method. Third, an effective algorithm to realize the maximum decomposition w.r.t. outputs is proposed. Finally, some examples are addressed to validate the theoretical results.
