Abstract
This paper regards function matrix projective synchronization of two different non-dissipatively coupled complex dynamical networks for different dimensions and different nodes. In this kind of complex dynamical networks the internal delays are different from the coupled delays. By using Lyapunov stability theory, using mathematical induction, two different hybrid feedback controllers are built to realize the function matrix projective synchronization. Compared with the existing results, the coupling matrices do not need to be symmetric or diffuse. By giving a numerical simulation we explain the validity and appropriateness of our conclusion.
Highlights
Lots of large systems in the real world, for example, biological neural networks, social networks, food chains and food webs, can be depicted by complex networks
The complex dynamical networks are composed of coupled nodes, in which all the nodes form the edge-connected nonlinear dynamic system
function projective synchronization (FPS) is the coupled drive and the response systems could be synchronized to the scale function matrix
Summary
Lots of large systems in the real world, for example, biological neural networks, social networks, food chains and food webs, can be depicted by complex networks. The research of complex networks (CNs) has drawn wide attention from scholars of various fields [1,2,3,4,5,6]. Synchronization as an important dynamic property of the coupled nonlinear systems has been extensively studied in [7,8,9,10,11]. FPS is the coupled drive and the response systems could be synchronized to the scale function matrix. If the scale function matrix is a unit matrix or a constant, we can obtain projective synchronization, complete synchronization or anti-synchronization. In the function matrix projective synchronization (FMPS) approach, the uncertainty of the scale function matrix can improve the security of communication [16, 17], FMS aroused wide interest of scholars
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