Maximal total population of species in a diffusive logistic model
Copyright policy )Maximal total population of species in a diffusive logistic model
In this paper, we investigate the maximization of the total population of a single species which is governed by a stationary diffusive logistic equation with a fixed amount of resources. For large diffusivity, qualitative properties of the maximizers like symmetry will be addressed. Our results are in line with previous findings which assert that for large diffusion, concentrated resources are favorable for maximizing the total population. Then, an optimality condition for the maximizer is derived based upon rearrangement theory. We develop an efficient numerical algorithm applicable to domains with different geometries in order to compute the maximizer. It is established that the algorithm is convergent. Our numerical simulations give a real insight into the qualitative properties of the maximizer and also lead us to some conjectures about the maximizer.
- University of Dundee United Kingdom
- Claremont McKenna College United States
- University of the Witwatersrand South Africa
Rearrangements, Population dynamics, PDEs in connection with biology, chemistry and other natural sciences, Gradient-based algorithm, 530, Optimal control, 510, Numerical methods based on necessary conditions, Diffusion, optimal control, Population dynamics (general), Logistic Models, gradient-based algorithm, population dynamics, rearrangements, Optimality conditions for problems involving partial differential equations, Diffusive logistic equation, diffusive logistic equation, Algorithms
Rearrangements, Population dynamics, PDEs in connection with biology, chemistry and other natural sciences, Gradient-based algorithm, 530, Optimal control, 510, Numerical methods based on necessary conditions, Diffusion, optimal control, Population dynamics (general), Logistic Models, gradient-based algorithm, population dynamics, rearrangements, Optimality conditions for problems involving partial differential equations, Diffusive logistic equation, diffusive logistic equation, Algorithms
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