Abstract
Resource limitations and density dependent releasing of natural enemies during the pest control and integrated pest management will undoubtedly result in nonlinear impulsive control. In order to investigate the effects of those nonlinear control strategies on the successful pest control, we have proposed a pest-natural enemy system concerning integrated pest management with density dependent instant killing rate and releasing rate. In particular, the releasing rate depicts how the number of natural enemy populations released was guided by their current density at the fixed moment. The threshold condition which ensures the existence and global stability of pest-free periodic solution has been discussed first, and the effects of key parameters on the threshold condition reveal that reducing the pulse period does not always benefit pest control; that is, frequent releasing of natural enemies may not be beneficial to the eradication of pests when the density dependent releasing method has been implemented. Moreover, the forward and backward bifurcations could occur once the pest-free periodic solution becomes unstable, and the system could exist with very complex dynamics. All those results confirm that the control actions should be carefully designed once the nonlinear impulsive control measures have been taken for pest management.
Highlights
Integrated pest management (IPM), known as integrated pest control (IPC), is a wide approach that integrates multiple control measures for economic control of pests
In order to investigate the effects of those nonlinear control strategies on the successful pest control, we have proposed a pest-natural enemy system concerning integrated pest management with density dependent instant killing rate and releasing rate
IPM aims to maintain the pest population below the economic injury level (EIL) by taking biological, chemical, and physical control tactics
Summary
Integrated pest management (IPM), known as integrated pest control (IPC), is a wide approach that integrates multiple control measures for economic control of pests. Pesticide pollution has been recognized as a major health hazard to human, it can seriously change the ecological system, and it may cause damage to nontarget organisms To combine these control measures together and to maximize control effects at minimum levels of control resources, a number of impulsive differential equations have been developed to investigate the dynamics of pest and enemies and to analyze the optimal control schemes [3, 4, 10,11,12,13]. The main purpose of the present paper is to focus on how the density dependent killing rate and density dependent releasing strategy affect the dynamics of the system and the effectiveness of the control measures Based on this purpose, we first investigate the threshold condition which guarantees the existence and global stability of pest-free periodical solution. The important results found in this work confirm that the control actions should be carefully designed once the nonlinear impulsive control measures have been taken for pest management
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