Multi-type synchronization of impulsive coupled oscillators via topology degree

Yingjie Bi; Zhidan Cai; Shuai Wang

Applications of Mathematics (2024)

  • Volume: 69, Issue: 2, page 185-207
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Bi, Yingjie, Cai, Zhidan, and Wang, Shuai. "Multi-type synchronization of impulsive coupled oscillators via topology degree." Applications of Mathematics 69.2 (2024): 185-207. <http://eudml.org/doc/299280>.

@article{Bi2024,
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.},
author = {Bi, Yingjie, Cai, Zhidan, Wang, Shuai},
journal = {Applications of Mathematics},
keywords = {synchronization; impulsive coupled oscillator; rotating periodic solution; impulsive system},
language = {eng},
number = {2},
pages = {185-207},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multi-type synchronization of impulsive coupled oscillators via topology degree},
url = {http://eudml.org/doc/299280},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Bi, Yingjie
AU - Cai, Zhidan
AU - Wang, Shuai
TI - Multi-type synchronization of impulsive coupled oscillators via topology degree
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 2
SP - 185
EP - 207
AB - 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.
LA - eng
KW - synchronization; impulsive coupled oscillator; rotating periodic solution; impulsive system
UR - http://eudml.org/doc/299280
ER -

References

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