2026/07/25 by Huaizhi Cao, Jiawei Chu, Hai-Yang Jin
#math.AP
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 \colorblackfor 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.