Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions

This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the controlled network to an extended network of N＋1 nodes without controls. It is shown that the controlled synchronizability of the given network is determined by the real part of the smallest nonzero eigenvalue of the coupling matrix of its extended network when the synchronized region is unbounded; but it is determined by the ratio of the real parts of the largest and the smallest nonzero eigenvalues of the coupling matrix when the synchronized region is bounded. Both theoretical analysis and numerical simulation show that the portion of controlled nodes has no critical values when the synchronized region is unbounded, but it has a critical value when the synchronized region is bounded. In the former case, therefore, it is possible to control the network to achieve synchronization by pinning only one node. In the latter case, the network can achieve controlled synchronization only when the portion of controlled nodes is larger than the critical value.

Does the eigenratio synchronizability of λ2/λN represent the a complex network？

In the study of complex networks, it is commonly believed that the eigenratio λ2/λN of the Laplacian matrix of a network represents the network synchronizability, especially for symmetric networks. This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region. Consequently, a simple answer is presented to the question of when the eigenratio λ2/λN does represent the network synchronizability.

Variation Characteristics of Regional Synchronous Wind in Hami,Xinjiang of Northwest China

From several towers in Hami, Xinjiang of Northwest China, built by the national wind power resources professional observation network, we selected three towers with synchronous 10-min average wind speed data for one year（May 2011-April 2012） under strict quality control. The towers are located where large-scale wind power development is projected. We analyzed the frequency and variation of extreme wind speed at low wind condition（LWC）, rated wind condition（RWC）, and cut-out wind condition（CWC）, which may significantly impact the electric power grid configuration in large-scale wind power development. The correlation between duration and frequency of LWC/RWC/CWC is obtained. Major findings are： 1） The frequency of CWC is the lowest among all conditions, its synchronous rate at all three towers tends to be zero, and the frequency of LWC is always greater than that of RWC. 2） Among the three towers, the synchronous rate of RWC steadily increases with height, and LWC differs little between different levels. The synchronous rate of LWC concentrates in winter, while that of RWC mainly occurs in spring and summer.Diurnal variation of LWC/RWC during the entire year is significantly different. 3） During the study year,the longest durations of synchronous LWC and RWC among the three towers are up to 640 and 700 min,respectively. The duration and frequency of LWC/RWC can be quantitatively well described by a logarithmic function. Consequently, the synchronous rates of LWC and RWC over any duration in the region can be easily calculated by using the fitting function equation from observed data. These results are of value to the planning of large-scale wind power transmission and grid dispatching in this area.

Pinning synchronization of networked multi-agent systems: spectral analysis

Pinning synchronization of a networked multi-agent system with a directed communication topology is investigated from a spectral analysis approach. Some new types of synchronized regions for networked systems with different nonlinear agent dynamics and inner coupling structures are discovered. The eigenvalue distributions of the coupling and control matrices for different types of directed networks are obtained. The effects of the network topology, pinning density and pinning strength on the network synchronizability are examined through extensive numerical simulations. It is shown that the synchronizability of the pinned network can be effectively improved by increasing pinning density and pinning strength for some types of synchronized regions, whereas too large the pinning density and pinning strength will lead to desynchronization for other types. It is found that directed random networks are not always easier to synchronize than directed small-world networks, and a denser eigenvalue distribution may not always imply better synchronizability.