Optimal control of boundary habitat hostility for interacting species

Abstract

We consider boundary control for a parabolic system describing the evolution of two interacting species in a bounded habitat. The control models the hostility of the boundary environment to the maintenance of the species. The objective functional represents the balance between the ecological benefit (modelled by the size of the two populations) and the economic cost of maintaining an ecologically favorable boundary environment (modelled by the boundary friendliness). The unique optimal control is characterized in terms of the solution of the optimality system, which consists of the state system coupled with an adjoint system. Copyright © 1999 John Wiley & Sons, Ltd.

Optimal Birth Control for an Age-Dependent Competition System of N Species

“…It is easy to prove that the following result is true. Lemma 1 If (β * , p * ) is a solution to problem (11), then for any given T > 0, (β * , p * ) is a solution to the following problem:…”

“…Since then, the control problem has received much attention from several researchers [2−9] . For the control problems of multi-species, Albrecht et al [10] , Lenhart et al [11] , and Crespo et al [12] considered several systems, respectively. Their results are not concerned with age factor.…”

“…which enables us to state Theorem 4 Let (β * , p * ) be a solution to problem (11), then there exist λ ∞ ≥ 0 and a function q : [0, ∞) → R n , not simultaneously zero, such that…”

Optimal birth control of free horizon problems for predator-prey system with age-structure

“…For the control problems of multi-species have been investigated in the literature (see [7][8][9]). K. Renee Fistera and Suzanne Lenhart [10] investigated optimal control of a first order partial differential equation (PDE) system representing a competitive population model with age structure.…”

Optimal harvesting for an age-dependent n-dimensional food chain model

“…The control problems of multi-species have also been investigated in Refs. [8][9][10], but their results are not concerned with age factor. Meng, et al [11] discussed the dynamics of an age structured predator-prey model with disturbing pulse and time delays.…”