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A Model Predator-Prey System with Mutual Interference and Time Delay

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Population Biology

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 52))

Abstract

The Gause predator-prey model (Freedman, 1980, Chapter 4) separates the specific growth rate of the prey from the predator functional response. Hassell (1971) and Rogers and Hassell (1974) introduced the notion of mutual interference of predators searching for prey. This idea was incorporated into the Gause predator-prey model in Freedman (1979). It was shown there that mutual interference is a “stabilizing” process.

This author wishes to acknowledge the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A4823 for partially supporting the research in this paper.

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References

  • Freedman, H.I. (1979): Stability analysis of a predator-prey system with mutual interference and density-dependent death rates, Bui. Math. Biol. 41: 67–78.

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  • Freedman, H.I. (1980): Deterministic Mathematical Models in Population Ecology, Marcel Dekker, Inc., New York.

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  • Freedman, H.I., and V.S.H. Rao (1983): The tradeoff between mutual interference and time lags in predator-prey systems, BuZ. Math. Biol. (in press).

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  • Hassell, M.P. (1971): Mutual interference between searching insect parasites, J. Anim. Ecol. 40: 473–486.

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  • May, R.M. (1973): Time-delay versus stability in population models with two and three trophic levels, Ecology 54: 315–325.

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  • Rogers, D.J., and M.P. Hassell (1974): General models for insect parasite and predator searching behaviour: interference, J. Anim. EcoZ. 43: 239–253.

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© 1983 Springer-Verlag Berlin Heidelberg

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Rao, V.S.H., Freedman, H.I. (1983). A Model Predator-Prey System with Mutual Interference and Time Delay. In: Freedman, H.I., Strobeck, C. (eds) Population Biology. Lecture Notes in Biomathematics, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87893-0_39

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  • DOI: https://doi.org/10.1007/978-3-642-87893-0_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12677-5

  • Online ISBN: 978-3-642-87893-0

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