Propagation of stochastic travelling waves of cooperative systems with noise

Hao Wen; Jianhua Huang; Yuhong Li

doi:10.3934/dcdsb.2021295

Article Contents

2022, Volume 27, Issue 10: 5779-5803. Doi: 10.3934/dcdsb.2021295

This issue Previous Article Modeling the second outbreak of COVID-19 with isolation and contact tracing Next Article Global strong solution to the nonhomogeneous micropolar fluid equations with large initial data and vacuum

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
^* Corresponding author: Jianhua Huang

Received: August 2021

Revised: October 2021

Early access: December 17, 2021

Published online: December 17, 2021

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 35R60, 37A25; Secondary: 60H15.

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