Evolution of dispersal and the analysis of a resource flourished
population model with harvesting
This study explores a spatially distributed harvesting model that
signifies the outcome of the competition of two competing 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.
Additionally, we have demonstrated the existence of positive periodic
states numerically that arise for seasonal changes or any other periodic
factors for time-dependent parameters.