标题：Periodic dynamics in a forager-exploiter system under homogeneous and heterogeneous resource environments
报告时间：2026年8月2日（星期日）10：00-11：00
报告地点：人民大街校区数学与统计学院619大应用数学实验室
主讲人： 金海洋
主办单位：数学与统计学院
报告内容简介：
We investigate time-periodic dynamics in a forager-exploiter system with a taxis cascade under both homogeneous and heterogeneous resource environments. The model describes the interactions among foragers, exploiters, and environmental resources, where foragers move toward higher resource densities while exploiters aggregate toward regions with higher forager densities. Our results show that different resource renewal mechanisms shape periodic dynamics in fundamentally different ways. Precisely, for time-periodic resource renewal rates, we establish the existence of positive time-periodic solutions for any positive renewal rate and further prove their global stability under suitable conditions on the parameters. In contrast, for homogeneous environments, only large resource renewal rates can destabilize the constant steady state through the Hopf bifurcation, thereby generating non-constant time-periodic solutions.
Interestingly, for spatially heterogeneous and temporally homogeneous environments, our numerical simulations indicate that spatial heterogeneity exhibits opposing effects on periodic dynamics depending on total resource availability. When resources are sufficiently abundant, spatial heterogeneity tends to suppress the emergence of temporal oscillations, whereas when resources are relatively scarce, it may instead promote oscillatory behaviors, and sufficiently concentrated local resource supplies can trigger local or even global temporal oscillations. These findings reveal a delicate interplay among resource renewal mechanisms, resource availability, and spatial heterogeneity in shaping dynamics behavior.
主讲人简介：
华南理工大学教授，博士生导师，国家级高层次青年人才，主要从事非线性偏微分方程的应用研究，获得广东省自然科学二等奖，广东省杰出青年基金，主持多项国家自然科学基金项目，在SIMA，SIAP，M3AS，JDE, Nonlinearity 等期刊上发表论文30多篇。
