title: A minimum model of prey-predator system with dormancy of predators and the paradox of enrichment.
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.
authors.affiliation: Graduate School of Human Development and Environment, Kobe University, Kobe, 657-8501, Japan. kuwamura@main.h.kobe-u.ac.jp
authors.forename: Masataka
authors.initials: M
authors.lastname: Kuwamura
authors.forename: Takefumi
authors.initials: T
authors.lastname: Nakazawa
authors.forename: Toshiyuki
authors.initials: T
authors.lastname: Ogawa
mesh_terms: D000818:Animals; D003621:Daphnia / Q000254:growth & development; D017753:Ecosystem; D005260:Female; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D011157:Population Dynamics; D011235:Predatory Behavior