Theoretical studies in cooperative phenomena and population ecology
We study problems in the stability of nonlinear ecological models and in the theory of collective motion in physical systems. We first establish criteria for global stability in deterministic nonlinear population models, including the most general criteria so far available for the Lotka-Volterra mod...
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| Format: | Others |
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PDXScholar
1976
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| Online Access: | https://pdxscholar.library.pdx.edu/open_access_etds/598 https://pdxscholar.library.pdx.edu/cgi/viewcontent.cgi?article=1597&context=open_access_etds |
| Summary: | We study problems in the stability of nonlinear ecological models and in the theory of collective motion in physical systems. We first establish criteria for global stability in deterministic nonlinear population models, including the most general criteria so far available for the Lotka-Volterra model. Next we study conditions for coexistence under periodic perturbations in population models and establish criteria for the appearance of dynamic equilibrium states. The third study in ecological stability establishes that a measure of the stability of population models in the presence of white noise is given by a Liapunov function for the nonlinear deterministic model, and the implications of the result are examined. We consider next the use of kinetic equations to study physical systems, and prove that the use of higher order derivatives in the Mori formalism leads to results formally identical with Mori's continued fraction theory. We then apply the method of using higher derivatives to develop a physical picture of collective mode dynamics in the linear Heisenberg chain. The collective modes and their time scales are isolated and studied. |
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