A minimum model of prey-predator system with dormancy of predators and the paradox of enrichment |
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Authors: | Masataka Kuwamura Takefumi Nakazawa Toshiyuki Ogawa |
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Institution: | (1) Graduate School of Human Development and Environment, Kobe University, Kobe 657-8501, Japan;(2) Center for Ecological Research, Kyoto University, Otsu 520-2113, Japan;(3) Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan |
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Abstract: | In this paper, a mathematical model of a prey-predator system is proposed to resolve the paradox of enrichment in ecosystems.
The model is based on the natural strategy that a predator takes, i.e, it produces resting eggs in harsh environment. Our
result gives a criterion for a functional response, which ensures that entering dormancy stabilizes the population dynamics.
It is also shown that the hatching of resting eggs can stabilize the population dynamics when the switching between non-resting
and resting eggs is sharp. Furthermore, the bifurcation structure of our model suggests the simultaneous existence of a stable
equilibrium and a large amplitude cycle in natural enriched environments.
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Keywords: | Prey-predator system Dormancy Hatching Eutrophication Saddle-node bifurcation |
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