Stochastic travelling wave solution of the $ N $-species cooperative systems with multiplicative noise

Hao Wen; Yantao Luo; Jianhua Huang; Yuhong Li; Hao Wen; Yantao Luo; Jianhua Huang; Yuhong Li

doi:10.3934/era.2023225

Electronic Research Archive

2023, Volume 31, Issue 8: 4406-4426. doi: 10.3934/era.2023225

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Research article

Stochastic travelling wave solution of the $ N $-species cooperative systems with multiplicative noise

1.
China Aerodynamics Research and Development Center, Mianyang 621000, China
2.
College of Science, National University of Defense Technology, Changsha 410073, China
3.
School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Received: 09 March 2023 Revised: 28 April 2023 Accepted: 21 May 2023 Published: 12 June 2023

The current paper is devoted to the stochastic $ N $-species cooperative system with a moderately strong noise. By the theory of monotone random systems and the technique of suitable marker of wavefront, the existence of the travelling wave solution is established. By applying the Feynman-Kac formula and sup-sub solution technique, the upper and lower bounded of the asymptotic wave speed are also obtained. Finally, we give an example for stochastic 3-species cooperative systems.
- N-species stochastic cooperative system,
- Feynman-Kac formula,
- stochastic travelling waves,
- asymptotic wave speed
Citation: Hao Wen, Yantao Luo, Jianhua Huang, Yuhong Li. Stochastic travelling wave solution of the $ N $-species cooperative systems with multiplicative noise[J]. Electronic Research Archive, 2023, 31(8): 4406-4426. doi: 10.3934/era.2023225

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Abstract

The current paper is devoted to the stochastic $ N $-species cooperative system with a moderately strong noise. By the theory of monotone random systems and the technique of suitable marker of wavefront, the existence of the travelling wave solution is established. By applying the Feynman-Kac formula and sup-sub solution technique, the upper and lower bounded of the asymptotic wave speed are also obtained. Finally, we give an example for stochastic 3-species cooperative systems.

References

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