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doi: 10.3934/dcdsb.2021295
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## Propagation of stochastic travelling waves of cooperative systems with noise

 1 College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China 2 School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

* Corresponding author: Jianhua Huang

Received  August 2021 Revised  October 2021 Early access December 2021

Fund Project: Supported by NSF of China (No.11771449, 12031020, 61841302) and NSF of Hunan Province, China (2020JJ4102)

We consider the cooperative system driven by a multiplicative It\^o type white noise. The existence and their approximations of the travelling wave solutions are proven. With a moderately strong noise, the travelling wave solutions are constricted by choosing a suitable marker of wavefront. Moreover, the stochastic Feynman-Kac formula, sup-solution, sub-solution and equilibrium points of the dynamical system corresponding to the stochastic cooperative system are utilized to estimate the asymptotic wave speed, which is closely related to the white noise.

Citation: Hao Wen, Jianhua Huang, Yuhong Li. Propagation of stochastic travelling waves of cooperative systems with noise. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021295
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