A diffusive single-species model with periodic coefficients and its optimal harvesting policy

In this paper, we consider a Logistic model with spatially nonhomogeneous diffusion under the exploitation∂u∂t-DΔu=r(x,t)u1-uK(x,t)-E(x,t)u,(x,t)∈Ω×(0,∞),u(x,0)=ϕ(x),x∈Ω,∂u∂n=0,t∈(0,∞),x∈∂Ω,where coefficients r, K, E are smooth T-periodic functions; this model describes the growth of the single species with the Neumann boundary condition and initial value condition. We investigate the global stability of a periodic solution and optimal harvesting policy. Furthermore, we also consider a generalized single-species model and its harvesting problem. The results gained in this article extend the works in references [Hailong Li, Logistic model for single-species with spatial diffusion and its optimal harvesting policy, J. Biomath., 14 (3) (1999) 293-300 (in Chinese); Ling Bai, Ke Wang, Gilpin-Ayala model with spatial diffusion and its optimal harvesting policy, Appl. Math. Comput., 171 (2005) 531-546].