Abstract
The switched discrete host-parasitoid model with Beverton-Holt growth concerning integrated pest management has been proposed, and the switches are guided by the economic threshold (ET). The integrated pest management (IPM) tactics are applied to prevent the economic injury if the density of host population exceeds the ET, and the IPM tactics are called off once the density of host population descends below ET. To begin with, the regular and virtual equilibria of switched system has been discussed by two or three parameter-bifurcation diagrams, which reveal the regions of different types of equilibria. Besides, numerical bifurcation analyses about inherent growth rates show that the switched discrete system may have complicated dynamics behavior including chaos and the coexistence of multiple attractors. Finally, numerical bifurcation analyses about killing rates indicate that the system comply with the Volterra principle, and initial values of both host and parasitoid populations affect the host outbreaks times.
Highlights
In recent years, integrated pest management (IPM) has been introduced as a long-term, more effective, and low-cost control strategy to reduce the pest damage which integrated with biological, cultural, and chemical tactics to control pest populations at the tolerable level [1, 2]
It is well known that frequently using pesticides kills pests effectively but may cause serious environmental problems and result in faster development of drug resistance
The integrated pest management as an approach to control insect pests must be committed to a long-term strategy which includes biological control and chemical control
Summary
In recent years, integrated pest management (IPM) has been introduced as a long-term, more effective, and low-cost control strategy to reduce the pest damage which integrated with biological, cultural, and chemical tactics to control pest populations at the tolerable level [1, 2]. IPM has been proved to be effective pest control strategies through theory analysis and experiments [3] It aims at alleviating the pollution of plants and animals due to the excessive use of pesticides. Chemical control (e.g., spaying pesticides) is an effective strategy to reduce the pest population [4]. Biological control is mainly adopted by periodically releasing its natural enemies, such as predators, parasitoids, or pathogen to keep pest population below the given economic threshold (ET). The main purpose of this paper is to construct the switched discrete host-parasitoid model with Beverton-Holt growth concerning integrated pest management (IPM), and the economic threshold (ET) is chosen to guide the switches. We establish a switching system to model the process of releasing natural enemies and spraying pesticides (or harvesting pest) guided by ET.
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