Journal of Mathematical Biology

, Volume 58, Issue 3, pp 459–479

A minimum model of prey-predator system with dormancy of predators and the paradox of enrichment

  • Masataka Kuwamura
  • Takefumi Nakazawa
  • Toshiyuki Ogawa

DOI: 10.1007/s00285-008-0203-1

Cite this article as:
Kuwamura, M., Nakazawa, T. & Ogawa, T. J. Math. Biol. (2009) 58: 459. doi:10.1007/s00285-008-0203-1


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.


Prey-predator systemDormancyHatchingEutrophicationSaddle-node bifurcation

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Masataka Kuwamura
    • 1
  • Takefumi Nakazawa
    • 2
  • Toshiyuki Ogawa
    • 3
  1. 1.Graduate School of Human Development and EnvironmentKobe UniversityKobeJapan
  2. 2.Center for Ecological ResearchKyoto UniversityOtsuJapan
  3. 3.Graduate School of Engineering ScienceOsaka UniversityOsakaJapan