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Global Synchronization of Complex Networks Perturbed by Brown Noises and Poisson Noises

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Abstract

Stochastic disturbances, such as Brown noises and Poisson noises, are ubiquitous in the real world. It is necessary to consider these noises’ effect for dynamical behaviors of complex networks. This paper addresses the synchronization problem for complex networks perturbed by Brown noises and Poisson noises. By utilizing the martingale theory such as the predictable projection operator and the dual predictable projection operator, we transform the expectation of the stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper presents a global synchronization criterion for complex networks perturbed by Brown noises and Poisson noises. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed approach.

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Acknowledgments

The authors would like to thank the Editor and the anonymous reviewers for their valuable comments and suggestions which improve the quality and presentation of this paper. The work of Y. Zhang and B. Song was supported by the National Natural Science Foundation of China under Grants 61104221 and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant 10KJB120004. The work of J.H. Park was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A1A2A10005201). The work of Z.G. Wu was supported by the National Natural Science Foundation of China under Grants 61174029.

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Authors and Affiliations

  1. School of Mathematics and Physics, Xuzhou Institute of Technology, Xuzhou , 221000, Jiangsu, People’s Republic of China

    Ya Zhang

  2. School of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou , 221116, Jiangsu, People’s Republic of China

    Ya Zhang & Bo Song

  3. Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan , 712-749, Republic of Korea

    Bo Song

  4. Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan , 712-749, Republic of Korea

    Ju H. Park

  5. School of Information Science and Engineering, Changzhou University, Changzhou , 213164, People’s Republic of China

    Guodong Shi

  6. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control Zhejiang University, Hangzhou , 310027, Zhejiang, People’s Republic of China

    Zheng -Guang Wu

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  1. Ya Zhang
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Correspondence to Ju H. Park.

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Zhang, Y., Song, B., Park, J.H. et al. Global Synchronization of Complex Networks Perturbed by Brown Noises and Poisson Noises. Circuits Syst Signal Process 33, 2827–2849 (2014). https://doi.org/10.1007/s00034-014-9781-x

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