Input-output analysis of mathematical models of ecosystems
Necessary and sufficient conditions for the convergence of the solutions of linear and nonlinear time varying compartmental models described by systems of differential equations are reviewed. For continuous and discrete models, the concept of environ analysis is extended to advanced linear systems and for the first time to systems with time varying coefficient matrices A(t) and (A(t))/sup T/. Output and input environ partitioning flow and storage matrices for a two trophic level aquatic system are derived in the form of integral equations. As a step towards the important goal of controlling the eutrophication phenomenon, two phytoplankton population models in natural waters are presented. In the first model, a non-linear function general enough to include the effects of feeding saturation intraspecific consumer interference, and eutrophication phenomenon is used to present the transfer of material or energy from phytoplankton to zooplankton populations. The model using this grazing rate function is subjected to equilibrium and stability analysis to ascertain its mathematical implications. It is shown that, for a certain range of one of the parameters in this function all equilibrium points of the system become stable even with nutrient enrichment. In the second model, dynamics of both nitrogen and phosphorus cycles are combined. The influence of direct human control added to different aquatic models is studied in detail. Optimal control theory is used to obtain optimal strategies for the control of these models with several cost functions. It is found that the control program in each problem depends on the model considered and on the function to be optimized.
- OSTI ID:
- 5030507
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
AQUATIC ECOSYSTEMS
MATHEMATICAL MODELS
EUTROPHICATION
CONTROL
DIFFERENTIAL EQUATIONS
INPUT-OUTPUT ANALYSIS
NITROGEN CYCLE
PHYTOPLANKTON
POPULATION DYNAMICS
ZOOPLANKTON
AQUATIC ORGANISMS
ECONOMIC ANALYSIS
ECONOMICS
ECOSYSTEMS
EQUATIONS
PLANKTON
520100* - Environment
Aquatic- Basic Studies- (-1989)