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Multi-type synchronization of impulsive coupled oscillators via topology degree

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Abstract

The existence of synchronization is an important issue in complex dynamical networks. In this paper, we study the synchronization of impulsive coupled oscillator networks with the aid of rotating periodic solutions of impulsive system. The type of synchronization is closely related to the rotating matrix, which gives an insight for finding various types of synchronization in a united way. We transform the synchronization of impulsive coupled oscillators into the existence of rotating periodic solutions in a relevant impulsive system. Some existence theorems about rotating periodic solutions for a non-homogeneous linear impulsive system and a nonlinear perturbation system are established by topology degree theory. Finally, we give two examples to show synchronization behaviors in impulsive coupled oscillator networks.

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Authors and Affiliations

  1. School of Science, Changchun University, Weixing Road, Chaoyang District, Changchun, 130022, P. R. China

    Yingjie Bi

  2. School of Mathematics and Statistics, Changchun University of Science and Technology, Weixing Road, Chaoyang District, Changchun, 130022, P. R. China

    Zhidan Cai & Shuai Wang

Authors
  1. Yingjie Bi
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  2. Zhidan Cai
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  3. Shuai Wang
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Corresponding author

Correspondence to Shuai Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 12101076, 11901056), Natural Science Foundation of Jilin Province (20210101159JC) and the fund of the Department of Education of Jilin Province (JJKH20230789KJ).

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Bi, Y., Cai, Z. & Wang, S. Multi-type synchronization of impulsive coupled oscillators via topology degree. Appl Math 69, 185–207 (2024). https://doi.org/10.21136/AM.2024.0183-23

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