Synchronization and Averaging Principle Of Stationary Solutions For Stochastic Differential Equations

Abstract

In this paper, we mainly construct a connection between synchronized systems and multi-scale equations, and then use the averaging principle as an intermediate step to obtain synchronization. This strategy solves the synchronization problem of dissipative stochastic differential equations, regardless of the structure of the noise. Moreover, the averaging principle of stationary solutions is also investigated, which is different from the averaging principle of solutions with the fixed initial values.

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Acknowledgments

The authors would like to thank Professor Ren Jiagang for his helpful discussions and suggestions. The authors are also grateful to the anonymous reviewer for detailed and valuable comments that help in depth to improve the quality of the paper. Research is supported by NSFs of China (No.11271013, 11471340, 10901065) and the Fundamental Research Funds for the Central Universities, HUST: 2016YXMS003.

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Correspondence to Jicheng Liu.

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Li, Z., Liu, J. Synchronization and Averaging Principle Of Stationary Solutions For Stochastic Differential Equations. Potential Anal (2020). https://doi.org/10.1007/s11118-020-09859-z

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Keywords

  • Synchronization
  • Averaging principle
  • Stationary solution
  • Multi-scale
  • Stochastic differential equations

Mathematics Subject Classification (2010)

  • 60H10
  • 34F05