Permanence and extinction of regime-switching predator-prey models

Jianhai Bao; Jinghai Shao

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arXiv · 1506.08943

Permanence and extinction of regime-switching predator-prey models

Jianhai Bao·Jinghai Shao

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Abstract

In this work we study the permanence and extinction of a regime-switching predator-prey model with Beddington-DeAngelis functional response. The switching process is used to describe the random changing of corresponding parameters such as birth and death rates of a species in different environments. Our criteria can justify whether a prey die out or not when it will die out in some environments and will not in others. Our criteria are rather sharp, and they cover the known on-off type results on permanence of predator-prey models without switching. Our method relies on the recent study of ergodicity of regime-switching diffusion processes.

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Jianhai Bao, Jinghai Shao. 2015-06-30. Permanence and extinction of regime-switching predator-prey models. https://arxiv.org/abs/1506.08943

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