Synchronization performance of complex oscillator networks

Outer synchronization between two complex dynamical networks with discontinuous coupling

In this paper, we study the outer synchronization between two complex networks with discontinuous coupling. Sufficient conditions for complete outer synchronization and generalized outer synchronization are obtained based on the stability theory of differential equations. The theoretical results show that two networks can achieve outer synchronization even if two networks are switched off sometimes and the speed of synchronization is proportional to the on-off rate. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results.

Reverse engineering of complex dynamical networks in the presence of time-delayed interactions based on noisy time series

Reverse engineering of complex dynamical networks is important for a variety of fields where uncovering the full topology of unknown networks and estimating parameters characterizing the network structure and dynamical processes are of interest. We consider complex oscillator networks with time-delayed interactions in a noisy environment, and develop an effective method to infer the full topology of the network and evaluate the amount of time delay based solely on noise-contaminated time series. In particular, we develop an analytic theory establishing that the dynamical correlation matrix, which can be constructed purely from time series, can be manipulated to yield both the network topology and the amount of time delay simultaneously. Extensive numerical support is provided to validate the method. While our method provides a viable solution to the network inverse problem, significant difficulties, limitations, and challenges still remain, and these are discussed thoroughly.

Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies

In this paper, the finite-time stochastic outer synchronization between two different complex dynamical networks with noise perturbation is investigated. By using suitable controllers, sufficient conditions for finite-time stochastic outer synchronization are derived based on the finite-time stability theory of stochastic differential equations. It is noticed that the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the settling time is also numerically demonstrated.

Performance of pinning-controlled synchronization

In this work we address the problem of controlling a complex network toward a synchronous evolution by using the pinning-control strategy. In considering this control approach, we investigate the effect of the number of pinned nodes and how the strategy performance behaves in accordance with the type of nodes that are chosen to be controlled. The roles of the control and coupling gains are also discussed.