Abstract
In this work, a synchronization scheme for networks of complex systems is presented. The proposed synchronization scheme uses a control law obtained with some definitions from graph theory and solving the Model-Matching Problem for complex networks. In particular, Rössler, Chen, Lorenz and Lü chaotic systems are used as complex chaotic systems into complex networks. Particular cases with regular and irregular networks of six identical chaotic systems are implemented, with some well-known topologies as star and ring small-world, and tree topologies. Highlighting, the obtained control law is applied to synchronize an irregular network of six different chaotic systems in a tree topology. The usefulness and advantages of the proposed synchronization scheme are highlighted performing numerical simulations of the chaotic complex networks.
Highlights
The field of synchronization of networks of complex systems has received a lot of attention in the last three decades, due to the potential applications in engineering, the proliferation of computer networks, communications networks as the internet, wireless communications as cellular telephony and many others [1, 2]
Model-Matching Control (MMC) has been used in the last years, but only to synchronize pairs of identical and nonidentical chaotic oscillators [11,12,13]
The aim of this work is devoted to demonstrate the effectiveness of the MMC for synchronizing networks of complex/chaotic systems in continuous-time
Summary
The field of synchronization of networks of complex systems has received a lot of attention in the last three decades, due to the potential applications in engineering, the proliferation of computer networks, communications networks as the internet, wireless communications as cellular telephony and many others [1, 2]. The aim of this work is devoted to demonstrate the effectiveness of the MMC for synchronizing networks of complex/chaotic systems in continuous-time This objective is achieved by using the model-matching approach from nonlinear control theory [17, 18] and extending the results in [11, 12]. An irregular Tree topology is realized using an array presented in Fig 12 with its associated coupling matrix Notice that it uses three different chaotic systems, two Lorenz systems, two Lusystems and two Chen systems.
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