3 research outputs found
Enhancing Population Persistence by a Protection Zone in a Reaction-Diffusion Model with Strong Allee Effect
Protecting endangered species has been an important issue in ecology. We
derive a reaction-diffusion model for a population in a one-dimensional bounded
habitat, where the population is subjected to a strong Allee effect in its
natural domain but obeys a logistic growth in a protection zone. We establish
the conditions for population persistence and extinction via the principal
eigenvalue of an associated eigenvalue problem and investigate the dependence
of this principal eigenvalue on the location (i.e., the starting point and the
length) of the protection zone. The results are used to design the optimal
protection zone under different boundary conditions, that is, to suggest the
starting point and length of the protection zone with respect to different
population growth rate in the protection zone, in order for the population to
persist in a long term