Abstract
In the famous continuous time random walk (CTRW) model, because of the finite lifetime of biological particles, it is sometimes necessary to temper the power law measure such that the waiting time measure has a convergent first moment. The CTRW model with tempered waiting time measure is the so-called tempered fractional derivative. In this article, we introduce the tempered fractional derivative into complex networks to describe the finite life span or bounded physical space of nodes. Some properties of the tempered fractional derivative and tempered fractional systems are discussed. Generalized synchronization in two-layer tempered fractional complex networks via pinning control is addressed based on the auxiliary system approach. The results of the proposed theory are used to derive a sufficient condition for achieving generalized synchronization of tempered fractional networks. Numerical simulations are presented to illustrate the effectiveness of the methods.
Highlights
In the past few decades, the study of fractional calculus has attracted substantial attention
The tempered fractional derivative is introduced to chaotic systems and complex networks
Synchronization of tempered fractional complex networks may be more useful in secure communication and control processing due to the addition of the tempered parameter. e pinning control scheme and auxiliary system approach are used to verify the existence of generalized synchronization in tempered fractional complex networks
Summary
In the past few decades, the study of fractional calculus has attracted substantial attention. E auxiliary system approach [27] was proposed to realize generalized synchronization between two complex networks. Synchronization of tempered fractional complex networks in a generalized sense leads to richer behavior than identical node dynamics in coupled networks. It may disclose a more complicated connection between the synchronized trajectories in the state spaces of coupled networks. We first study the tempered fractional complex network and its generalized synchronization. Ird, tempered fractional chaotic systems have more alterable dynamical behaviors than fractional ones It may be more useful in secure communication and control processing. An auxiliary system approach is used to consider the generalized synchronization for fractional complex networks.
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