Name
Abstract | ||
|---|---|---|
We consider the mathematical formulation, analysis, and numerical solution of an optimal control problem for a nonlinear “nutrient-phytoplankton-zooplankton-fish” reaction-diffusion system. We study the existence of optimal solutions, derive an optimality system, and determine optimal solutions. In the original spatially homogeneous formulation [M. Scheffer, Oikos, 62 (1991), pp. 271-282] the dynamics of plankton were investigated as a function of parameters for nutrient levels and fish predation rate on zooplankton. In our paper the model is spatially extended and the parameter for fish predation treated as a multiplicative control variable. The model has implications for the biomanipulation of food-webs in eutrophic lakes to help improve water quality. In order to illustrate the control of irregular spatiotemporal dynamics of plankton in the model we implement a semi-implicit (in time) finite element method with “mass lumping” and present the results of numerical experiments in two space dimensions. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1137/050645415 | SIAM J. Control and Optimization |
Keywords | Field | DocType |
nutrient-phytoplankton-zooplankton-fish system,original spatially homogeneous formulation,optimal control problem,fish predation,numerical experiment,optimal solution,optimality system,multiplicative control variable,optimal control,mathematical formulation,fish predation rate,numerical solution,finite element,food web,finite element method | Zooplankton,Phytoplankton,Plankton,Applied mathematics,Mathematical optimization,Optimality criterion,Optimal control,Control theory,Biomanipulation,Finite element method,Control variable,Mathematics | Journal |
Volume | Issue | ISSN |
46 | 3 | 0363-0129 |
Citations | PageRank | References |
7 | 0.85 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcus R. Garvie | 1 | 28 | 5.09 |
| Catalin Trenchea | 2 | 48 | 9.69 |