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Bennett, Jamie J. R.; Sherratt, Jonathan A.

How do dispersal rates affect the transition from periodic to irregular spatio-temporal oscillations in invasive predator-prey systems? (English) Zbl 1411.92242

Appl. Math. Lett. 94, 80-86 (2019).
Summary: When one considers the spatial aspects of a cyclic predator-prey interaction, ecological events such as invasions can generate periodic travelling waves (PTWs)–sometimes known as wavetrains. In certain instances PTWs may destabilise into spatio-temporal irregularity due to convective type instabilities, which permit a fixed width band of PTWs to develop behind the propagating invasion front. In this paper, we detail how one can locate this transition when one has unequal predator and prey dispersal rates. We do this by using absolute stability theory combined with a recent derivation of the amplitude of PTWs behind invasion. This work is applicable to a wide range of reaction-diffusion type predator-prey models, but in this paper we apply it to a specific set of equations (the Leslie-May model). We show that the width of PTW band increases/decreases when the ratio of prey and predator dispersal rates is large/small.

Cited in 3 Documents

MSC:

92D25 Population dynamics (general)
92D40 Ecology
35C07 Traveling wave solutions

Keywords:

periodic travelling waves; spatiotemporal irregularity; invasion; band width; predator-prey

Software:

PRED_PREY
Cite Review PDF
Full Text: DOI

References:

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