Forced waves and gap formations for a three-species competitive-cooperative system with nonlocal dispersal and shifting habitats

Rui Yan; Guirong Liu; Fangping Guo; Xiaocui Li; Rui Yan; Guirong Liu; Fangping Guo; Xiaocui Li

doi:10.3934/math.2026755

AIMS Mathematics

2026, Volume 11, Issue 6: 18580-18599. doi: 10.3934/math.2026755

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Research article

Forced waves and gap formations for a three-species competitive-cooperative system with nonlocal dispersal and shifting habitats

1.
School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
2.
School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China
3.
Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan 030006, China
4.
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China

Received: 27 March 2026 Revised: 25 May 2026 Accepted: 08 June 2026 Published: 24 June 2026
MSC : 35K57, 35C07, 92D40

This paper is concerned with the existence of forced waves and gap formations for a three-species competitive-cooperative system with nonlocal dispersal under habitat shifting at a constant speed, in which two species cooperate with each other while simultaneously competing with the third species together. First, the existence of forced waves is established by means of iterative techniques, where the speed lies within a specified interval. In the existence part, kernel functions are asymmetric, and the growth functions are allowed to be sign-preserving. Then, under the conditions that the kernel functions are symmetric and that the growth functions change sign, the gap formations are derived via a comparison principle.
- competitive-cooperative system,
- nonlocal dispersal,
- shifting habitat,
- forced waves,
- gap formations
Citation: Rui Yan, Guirong Liu, Fangping Guo, Xiaocui Li. Forced waves and gap formations for a three-species competitive-cooperative system with nonlocal dispersal and shifting habitats[J]. AIMS Mathematics, 2026, 11(6): 18580-18599. doi: 10.3934/math.2026755

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Abstract

This paper is concerned with the existence of forced waves and gap formations for a three-species competitive-cooperative system with nonlocal dispersal under habitat shifting at a constant speed, in which two species cooperate with each other while simultaneously competing with the third species together. First, the existence of forced waves is established by means of iterative techniques, where the speed lies within a specified interval. In the existence part, kernel functions are asymmetric, and the growth functions are allowed to be sign-preserving. Then, under the conditions that the kernel functions are symmetric and that the growth functions change sign, the gap formations are derived via a comparison principle.

References

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