Multiple stable equilibria in a predator-prey system |
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Authors: | Gary W Harrison |
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Institution: | (1) Department of Mathematics, College of Charleston, 29424 Charleston, SC, USA |
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Abstract: | Necessary and sufficient conditions are given for three equilibria to occur in a predatorprey model and conditions are given
for two of these to be stable. The existence of two stable equilibria requires predator intraspecific competition for either
space or food, and the lower the prey growth rate the stronger this predator self-regulation must be. A prey growth rate that
is skewed to the right, the ability of a few predators to survive at low prey densities, and predators with high searching
effectiveness, long handling times, and large maximum per capita rate of increase all make two stable equilibria more likely. |
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