Zahan Ishrat, Kamrujjaman Md
Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka 1000, Bangladesh.
Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh.
Heliyon. 2024 May 8;10(10):e30737. doi: 10.1016/j.heliyon.2024.e30737. eCollection 2024 May 30.
This study explores a spatially distributed harvesting model that signifies the outcome of the competition of two species in a heterogeneous environment. The model is controlled by reaction-diffusion equations with resource-based diffusion strategies. Two different situations are maintained by the harvesting effects: when the harvesting rates are independent in space and do not exceed the intrinsic growth rate; and when they are proportional to the time-independent intrinsic growth rate. In particular, the competition between both species differs only by their corresponding migration strategy and harvesting intensity. We have computed the main results for the global existence of solutions that represent either coexistence or competitive exclusion of two competing species depending on the harvesting levels and different imposed diffusion strategies. We also established some estimates on harvesting efforts for which coexistence is apparent. Also, some numerical results are exhibited in one and two spatial dimensions, which shed some light on the ecological implementation of the model.
本研究探索了一种空间分布的收获模型，该模型表征了在异质环境中两个物种竞争的结果。该模型由具有基于资源的扩散策略的反应扩散方程控制。收获效应维持了两种不同的情况：收获率在空间上独立且不超过内在增长率时；以及收获率与与时间无关的内在增长率成比例时。特别地，两个物种之间的竞争仅因其相应的迁移策略和收获强度而有所不同。我们计算了代表两个竞争物种共存或竞争排斥的解的全局存在性的主要结果，这取决于收获水平和不同的施加扩散策略。我们还建立了一些关于明显共存的收获努力的估计。此外，在一维和二维空间中展示了一些数值结果，这为该模型的生态应用提供了一些启示。
