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arXiv · 2607.22986

Parabolic-elliptic reduction suppresses Hopf bifurcation in a forager-exploiter system with cascade taxis

Huaizhi Cao·Jiawei Chu·Hai-Yang Jin
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Abstract

We study a parabolic-elliptic forager-exploiter model describing the cascade interaction between two species through a shared environmental resource with a constant renewal rate. We first establish the global existence and uniform boundedness of classical solutions in arbitrary dimensions {\color{black}for large initial population data and large taxis sensitivity coefficients. We then investigate the long-time behavior of solutions.} When the resource renewal rate is small, all solutions will converge exponentially to the unique constant steady state. Furthermore, for large resource renewal rates, the parabolic-elliptic system does not undergo Hopf bifurcation, which is in sharp contrast to the corresponding fully parabolic case, where temporal oscillations arise via Hopf bifurcation.

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Huaizhi Cao, Jiawei Chu, Hai-Yang Jin. 2026-07-25. Parabolic-elliptic reduction suppresses Hopf bifurcation in a forager-exploiter system with cascade taxis. https://arxiv.org/abs/2607.22986

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