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Discrete Switching Host-Parasitoid Models with Integrated Pest Control

Key Laboratory of Biologic Resources Protection and Utilization, Hubei Minzu University, Enshi, Hubei 445000, P. R. China

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Zhongyi Xiang

Key Laboratory of Biologic Resources Protection and Utilization, Hubei Minzu University, Enshi, Hubei 445000, P. R. China

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Sanyi Tang

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R. China

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, and

Jianhong Wu

Laboratory for Industrial and Applied Mathematics (LIAM), Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada

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https://doi.org/10.1142/S0218127414501144Cited by:15 (Source: Crossref)

Abstract

The switched discrete host-parasitoid model concerning integrated pest management (IPM) has been proposed in the present work, and the economic threshold (ET) is chosen to guide the switches. That is, if the density of host (pest) population increases and exceeds the ET, then the biological and chemical tactics are applied together. Those multiple control measures are suspended once the density of host falls below the ET. Firstly, the existence and stability of several types of equilibria of switched system have been discussed briefly, and two- or three-parameter bifurcation diagrams reveal the regions of different types of equilibria including regular and virtual equilibria. Secondly, numerical bifurcation analyses show that the switched discrete system may have very complex dynamics including the co-existence of multiple attractors and switched-like behavior among attractors. Finally, we address how the key parameters and initial values of both host and parasitoid populations affect the host outbreaks, switching frequencies or mean switching frequency, and consequently the relative biological implications with respect to pest control are discussed.

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