Fuzzy Complex Dynamical Networks and Its Synchronization

Abstract

Abstract-In this paper, the robust synchronization problem of fuzzy complex dynamical networks is investigated. A fuzzy complex dynamical network is an extension to an uncertain complex dynamical network in which all sources of parametric uncertainties are modeled with fuzzy numbers, i.e., all nodes' dynamics are described by fuzzy differential equations (FDEs) that permit a better description of a real process occurring in the presence of inaccuracy. To resolve the synchronization problem, this paper introduces new adaptive and impulsive controllers in which globally exponential synchronization of fuzzy dynamical networks under easily verified conditions is guaranteed. Moreover, we propose an efficient method that helps to find certain suitable nodes to be impulsively controlled via pinning, noting that these nodes, in general, vary at distinct impulsive time instants. Therefore, by using adaptive controllers and applying impulsive controllers to only a small portion of nodes, the whole network will completely be synchronized to a certain objective state. Finally, two numerical examples are given to illustrate the effectiveness of the proposed controllers.

Synchronization Criteria for Complex Dynamical Networks with State and Coupling Time‐Delays

“…Each node of the network can be a nonlinear dynamical system and create a complex dynamical network (CDN), which has been widely applied to model many complex systems. In the past few decades, the study of CDNs has received increasing attention from researchers in various disciplines, such as physics, mathematics, engineering, biology and sociology .…”

“…widely applied to model many complex systems. In the past few decades, the study of CDNs has received increasing attention from researchers in various disciplines, such as physics, mathematics, engineering, biology and sociology [9][10][11][12][13].…”

Pinning Synchronization Control of Two Fuzzy Complex Dynamical Networks based on Output Signals

“…Mukhija et al [23] studied a class of fuzzy complex networks with time-varying delay, and proposed new synchronization criteria. Mahdavi et al [24] designed an adaptive pulse controller for synchronization of fuzzy complex network, and proposed a method to choose suitable nodes to be controlled. However, pinning synchronization control has not been applied to two fuzzy complex dynamical networks.…”

Generalized Mutual Synchronization between Two Controlled Interdependent Networks

“…In the existing literature, it has been recognized that the network topology plays a significant role in synchronizability of diffusively coupled complex networks [7,8]. Also, by using some effective control schemes, a variety of synchronization phenomena have been discovered in various complex networks (see [9][10][11][12][13][14][15][16][17][18] and relevant references therein). However, the studies mentioned above focused almost exclusively on the inner synchronization inside a single, noninteracting network.…”