PMID: 8589541Jan 15, 1996Paper

Spatially heterogeneous discrete waves in predator-prey communities over a patchy environment

Mathematical Biosciences
D KohJ Wu

Abstract

A model motivated by the earlier work of J. D. Murray and D. Stirzaker is proposed to describe the dynamics of predator-prey communities over a patchy environment. The model is a system of delay differential equations. It is shown that if only one time lag is incorporated into the model, then a branch of spatially homogeneous periodic solutions occur as a primary Hopf bifurcation. However, if two time lags are used to measure different delayed factors in the process of growth, decay, and predator consumption of the prey population, then stable spatially heterogeneous periodic solutions (discrete waves or phase-locked oscillations) may exist. The utilized method is based on center manifold, normal form, and equivariant Hopf bifurcation theory.

References

Jul 1, 1989·Mathematical Biosciences·H I FreedmanY Takeuchi
Jan 1, 1986·Bulletin of Mathematical Biology·Y Takeuchi
Jan 1, 1987·Bulletin of Mathematical Biology·E Beretta, Y Takeuchi
Aug 1, 1984·Theoretical Population Biology·F M Stewart, B R Levin
Jun 1, 1951·Biometrika·J G SKELLAM

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