Global synchronization of complex networks perturbed by the Poisson noise

In this paper, the problem of stochastic synchronization analysis is investigated for complex networks perturbed by the Poisson noise. By using the key tool such as the infinites-imal operator for stochastic differential equations driven by the Poisson process, this paper proposes a globally exponentially synchronization criterion in mean square for complex networks perturbed by the Poisson noise. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed approach. As is known to all, complex dynamical networks (CDNs) widely exist in the real world, including food-webs, ecosystems, metabolic pathways, the Internet, the World Wide Web, social networks and global economic markets [1,2]. Since the discoveries of the small-world feature [3] and the scale-free feature [4] of complex networks, the analysis and the control of the dynamical behaviors in complex networks have been extensively investigated in the past decades. As a significant collective behavior, the studies on the synchronization phenomena of complex dynamical networks have gained considerable research interests [5–12]. On the other hand, in the real world, complex networks are often subject to environmental disturbances; especially the signal transfer within complex networks is always affected by the stochastic perturbations. Therefore, in order to reflect more realistic dynamical behaviors, many researchers have recently investigated the synchronization problems of complex networks perturbed by stochastic noises. For instance, complex networks perturbed by Brown noises have been discussed in [13–16]. The synchronization problems of discrete-time stochastic complex networks with Brown noises were investigated in [13,14]. As to the continuous case, the global exponential synchronization problem for complex dynamical networks with nonidentical nodes and Brown perturbations was studied in [15]. And the synchronization control problem for the competitive complex networks with Brown noises was investigated in [16]. However, it is well known that in the real world, beside Brown noises, there is a very common but important kind of random noises: Poisson noises. Poisson noises can be widely found in various applications such as neurophysiology systems, storage systems, queueing systems, economic systems, and so on [17,18]. It should be pointed out that, unlike the Brown process whose almost all sample paths are continuous, the Poisson process N ðtÞ is a jump process and has the sample paths which are right-continuous and have left limits (i.e. càdlàg). Therefore, there is a great difference between the stochastic integral with respect to the Brown process and the one with respect to the Poisson process. As a result, …