Stochastic travelling wave of three-species competitive–cooperative systems with multiplicative noise

Abstract

This paper is devoted to the stochastic travelling wave solutions of a three-species competitive–cooperative system with multiplicative noise. The existence of the travelling wave solutions can be proved by constructing upper/lower-solution and stochastic dynamical systems theory. Moreover, under the more restricted assumption on the coefficients of system, and applying Feynman–Kac formula and upper/lower solution technique, the upper/lower bounds of the asymptotic wave speed can be provided.

Keywords:

• Stochastic competition–cooperation system
• travelling wave solution
• upper/lower solution
• asymptotic wave speed
• Feynman–Kac formula

Mathematical Subject Classifications:

• 35R60
• Secondary: 60H15

Acknowledgments

We would like to thank the editors and anonymous referees for helpful comments and valuable suggestions to improve our manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by Natural Science Foundation of China (Nos. 11771449, 12031020) and National Natural Science Foundation of China (12171214, 11701242), the National Science Foundation of Gansu Province of China (21JR7RA535, 21JR7RA537) and the Fundamental Research Funds for the Central Universities (lzujbky-2023-37).