AI 中文总结
研究抛物-椭圆型觅食者-剥削者模型，通过建立经典解性质及研究长期行为，发现资源更新率小时解收敛到稳态，大时该系统无霍普夫分岔，与全抛物型情况不同。
AI 中文摘要
我们研究了一个抛物-椭圆型觅食者-剥削者模型，该模型描述了两个物种通过具有恒定更新率的共享环境资源进行的级联相互作用。首先，在任意维度下，对于大的初始种群数据和大的趋化敏感性系数，建立了经典解的全局存在性和一致有界性。然后研究了解的长期行为。当资源更新率较小时，所有解将指数收敛到唯一的常数稳态。此外，对于大的资源更新率，抛物-椭圆型系统不会经历霍普夫分岔，这与相应的全抛物型情况形成鲜明对比，在全抛物型情况中会通过霍普夫分岔出现时间振荡。
英文摘要
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.
