Stability criteria for multispecies ecological communities. Environmental Sciences Division publication No. 1226
This dissertation is a theoretical tour through various aspects of the stability of population models that represent communities of interacting species. This work seeks to gain general insight into ecological phenomena with the help of mathematical models. The models used are general and abstract nonlinear systems of equations. The main theme involves the development of stability conditions that are easily interpreted in terms of population parameters. These are expressed as simple constraints on the coefficients of the population equations in a small region near the equilibrium where the equations may be considered to be linear. The stability conditions presented are necessary and sufficient for the stability of mutualistic communities, a class that has not been considered in the ecological literature previously. These conditions are also sufficient for stability of ecological communities with any type of interspecies interactions. The applicability of these conditions to predator-prey and competition communities is explored with Monte Carlo computer experiments. The stability results are shown to be important in determining global stability. This is accomplished using the Lyapunov direct method from the theory of ordinary differential equations.
- Research Organization:
- Oak Ridge National Lab., TN (USA)
- DOE Contract Number:
- W-7405-ENG-26
- OSTI ID:
- 6587914
- Report Number(s):
- ORNL/TM-6475
- Resource Relation:
- Other Information: Thesis. Submitted by W.M. Post to Univ. of Tennessee, Knoxville
- Country of Publication:
- United States
- Language:
- English
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