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The trade-off between mutual interference and time lags in predator-prey systems

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We present a Gause predator-prey model incorporating mutual interference among predators, a density-dependent predator death rate and a time lag due to gestation. It is well known that mutual interference is stabilizing, whereas time delays are destabilizing. We show that in combining the two, a long time-lag usually, but not always, destabilizes the system. We also show that increasing delays can cause a bifurcation into periodic solutions.

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Research for this paper was partly supported by the Natural Science and Engineering Council of Canada, grant No. NSERC A4823, and by a grant from the University Grants Commission, New Delhi, India, grant No. F. 23-1174/79 (S.R. II).

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Freedman, H.L., Sree Hari Rao, V. The trade-off between mutual interference and time lags in predator-prey systems. Bltn Mathcal Biology 45, 991–1004 (1983).

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