Complex Projective Synchronization in Drive-Response Stochastic Complex Networks by Impulsive Pinning Control

The complex projective synchronization in drive-response stochastic coupled networks with complex-variable systems is considered. The impulsive pinning control scheme is adopted to achieve complex projective synchronization and several simple and practical sufficient conditions are obtained in a general drive-response network. In addition, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical simulations are provided to show the effectiveness and feasibility of the proposed methods

Exponential Synchronization of Stochastic Complex Dynamical Networks with Impulsive Perturbations and Markovian Switching

This paper investigates the exponential synchronization problem of stochastic complex dynamical networks with impulsive perturbation and Markovian switching. The complex dynamical networks consist of κ modes, and the networks switch from one mode to another according to a Markovian chain with known transition probability. Based on the Lyapunov function method and stochastic analysis, by employing M-matrix approach, some sufficient conditions are presented to ensure the exponential synchronization of stochastic complex dynamical networks with impulsive perturbation and Markovian switching, and the upper bound of impulsive gain is evaluated. At the end of this paper, two numerical examples are included to show the effectiveness of our results

Impulsive mean square exponential synchronization of stochastic dynamical networks with hybrid time-varying delays

This paper investigates the mean square exponential synchronization problem for complex dynamical networks with stochastic disturbances and hybrid time-varying delays, both internal delay and coupling delay are considered in the model. At the same time, the coupled time-delay is also probabilistic in two time interval. Impulsive control method is applied to force all nodes synchronize to a chaotic orbit, and impulsive input delay is also taken into account. Based on the theory of stochastic differential equation, an impulsive differential inequality and some analysis techniques, several simple and useful criteria are derived to ensure mean square exponential synchronization of the stochastic dynamical networks. Furthermore, pinning impulsive strategy is studied. An effective method is introduced to select the controlled nodes at each impulsive constants. Numerical simulations are exploited to demonstrate the effectiveness of the theory results in this paper

Synchronization of fractional chaotic complex networks with delays

summary:The synchronization of fractional-order complex networks with delay is investigated in this paper. By constructing a novel Lyapunov-Krasovskii function $V$ and taking integer derivative instead of fractional derivative of the function, a sufficient criterion is obtained in the form of linear matrix inequalities to realize synchronizing complex dynamical networks. Finally, a numerical example is shown to illustrate the feasibility and effectiveness of the proposed method

Drive network to a desired orbit by pinning control

summary:The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays the different influences and contributions of the various nodes in synchronization seeking processes of the dynamical network. Furthermore, it is shown that in order to drive a complex network to a desired synchronization state, the coupling strength should vary according to the controller. In addition, the theoretical results about the time-invariant network is extended to the time-varying network, and the result on synchronization problem can also be extended to the consensus problem of networked multi-agent systems. Subsequently, the theoretic results are illustrated by a typical scale-free (SF) neuronal network. Numerical simulations with three kinds of the homogenous solutions, including an equilibrium point, a periodic orbit, and a chaotic attractor, are finally given to demonstrate the effectiveness of the proposed control methodology