Synchronized stationary distribution of stochastic multi-group models with dispersal

  • Yan Liu
  • Anran Liu
  • Wenxue LiEmail author
Original Article


This paper is concerned with a new stationary distribution named synchronized stationary distribution. It is the first time to apply such kind of distribution to stochastic multi-group models with dispersal. And the existing region of synchronized stationary distribution is closely related to the coupling structure, stochastic disturbance intensity as well as the coefficients of models. We propose two main theorems to ensure the existence of a synchronized stationary distribution by combining Kirchhoff’s Matrix Tree Theorem in the graph theory as well as the Lyapunov method. Additionally, the value of our results is shown by applying them to stochastic coupled oscillators and stochastic coupled Rössler-like circuits with multiple dispersal. Correspondingly, two numerical examples are given to illustrate that our results are feasible and effective.


Synchronized stationary distribution Kirchhoff’s Matrix Tree Theorem Stochastic multi-group models Stochastic coupled oscillators 



The authors really appreciate the valuable comments of editors and reviewers. This work was supported by Shandong Province Natural Science Foundation (Nos. ZR2018MA005, ZR2018MA020, ZR2017MA008); the Key Project of Science and Technology of Weihai (No. 2014DXGJMS08), the Project of Shandong Province Higher Educational Science and Technology Program of China (No. J18KA218) and the Innovation Technology Funding Project in Harbin Institute of Technology (No. HIT.NSRIF.201703).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of Technology (Weihai)WeihaiPeople’s Republic of China

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