Modeling Population Dynamics with Volterra-Lotka Equations
نویسنده
چکیده
The purpose of this project is to model multi-species interactions using Volterra-Lotka equations in both two and three dimensions. Changes in population dynamics that arise as a result of modifying parameters are examined. The population dynamics of the resulting systems are analyzed in terms of stability around equilibrium points and within invariant surfaces. Of particular interest is periodic behavior and the initial conditions that lead to it. The two-dimensional system is found to exhibit stable periodic behavior for all initial conditions where neither population count is zero. The behavior of the three-dimensional system varies depending on the choice of constants used in the system definition. One case results in stable periodic behavior for all non-zero initial conditions, one case leads to the extinction of the top level predator and periodic stability for the remaining species, and the third case leads to unbounded growth for the bottom level prey and top level predator populations, and increasingly wild fluctuations in the population of the intermediate predator/prey population. The merits and flaws of these models are also discussed.
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