Abstract
This paper discusses the out lag synchronization of fractional order complex networks (FOCN) including both internal delay and coupling delay and with the employment of pinning control scheme. Using comparison theorem and constructing the auxiliary function, several synchronization criterions by linear feedback pinning control are presented. The model and the obtained results in this work are more general than the previous works. Correctness and effectiveness of the theoretical results are validated through numerical simulations.
Highlights
Complex networks (CN) have attracted great attentions due to their tremendous potentials in deferent fields, such as social organizations, World Wide Web, power grids, communication networks, and biological networks [1,2,3,4]
The existing results are mainly achieved on the case of “inner synchronization” where all nodes can gain a coherent dynamical behavior within a network
Some excellent conclusions about out synchronization in complex dynamical networks have been presented in the existing literatures [12,13,14]
Summary
Complex networks (CN) have attracted great attentions due to their tremendous potentials in deferent fields, such as social organizations, World Wide Web, power grids, communication networks, and biological networks [1,2,3,4]. Compared with classical ordinary differential networks, fractional calculus provides an excellent instrument to depict memory and hereditary properties in processing. Taking these factors into account, many scientists have introduced fractional differential and integrals to complex dynamical networks, forming fractional-order complex networks (FOCN). Using centralized and decentralized data-sampling principles and the theory of fractional differential systems, out synchronization in FOCN was considered in [18]. Time delay is inevitable in real networks due to finite information transmission and processing speeds among the units Inspired by the above discussions, the goal of this work is to consider out lag synchronization of FOCN with both node delay and coupling delay through the use of pinning control. The main contributions of this paper are listed as follows. (1) In order to form a general model, node delay and coupling delay are incorporated into the fractional order model. (2)The theory of fractional order differential equations and some new analysis techniques are employed to obtain novel sufficient conditions. (3)Out lag synchronization scheme is adopted to perform synchronization between two complex networks
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