Global boundedness and large time behavior in a forager-exploiter model of parabolic-parabolic-elliptic type

Yifeng Xiong; Lu Xu; Yifeng Xiong; Lu Xu

doi:10.3934/mbe.2026039

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 4: 1050-1066. doi: 10.3934/mbe.2026039

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Research article

Global boundedness and large time behavior in a forager-exploiter model of parabolic-parabolic-elliptic type

Yifeng Xiong ¹,
Lu Xu ^{1,2
,
,}

1.
College of Mathematics and Statistics, Yili Normal University, Yining 835000, China
2.
Institute of Applied Mathematics, Yili Normal University, Yining 835000, China

Received: 04 January 2026 Revised: 14 February 2026 Accepted: 24 February 2026 Published: 04 March 2026

This paper deals with the parabolic–parabolic–elliptic forager–exploiter model under homogeneous Neumann boundary conditions. It is shown that if the taxis effects of exploiters are suitably weak, its classical solution is globally bounded in arbitrary dimensions. Moreover, the foragers and exploiters will approach spatially homogeneous distributions in the large time limit.
- forager-exploiter model,
- boundedness,
- large time behavior
Citation: Yifeng Xiong, Lu Xu. Global boundedness and large time behavior in a forager-exploiter model of parabolic-parabolic-elliptic type[J]. Mathematical Biosciences and Engineering, 2026, 23(4): 1050-1066. doi: 10.3934/mbe.2026039

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Abstract

This paper deals with the parabolic–parabolic–elliptic forager–exploiter model under homogeneous Neumann boundary conditions. It is shown that if the taxis effects of exploiters are suitably weak, its classical solution is globally bounded in arbitrary dimensions. Moreover, the foragers and exploiters will approach spatially homogeneous distributions in the large time limit.

References

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