Abstract
A generalized predator-prey model concerning integrated pest management and nonlinear impulsive control measures is proposed and analyzed. The main purpose is to understand how resource limitation affects the successful pest control and pest outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given firstly. Once the threshold value exceeds a critical level, both pest and its natural enemy populations can oscillate periodically. Secondly, in order to address how the limited resources affect the pest control, as an example the Holling II functional response function is chosen. The numerical results show that predator-prey model with limited resource has complex dynamical behavior. In addition, it is confirmed that the model has the coexistence of pests and natural enemies for a wide range of parameters.
Highlights
During the last few decades, controlling insect pests of agriculture and insect vectors of important plant has been becoming an increasing important issue all over the world
Integrated pest management (IPM) involves choosing appropriate tactics from a range of pest control techniques including biological, cultural, and chemical methods to suit individual cropping systems, pest complexes, and local environments [1,2,3,4]. It has been proved both theoretically [2, 5] and experimentally [6, 7] that IPM has been more effective than the biological control or chemical control alone
In this contribution we focus on a generalized predatorprey model under limited resource; the main purpose of this paper is to understand the effect of resource limitation on outbreaks of a pest population
Summary
During the last few decades, controlling insect pests of agriculture and insect vectors of important plant has been becoming an increasing important issue all over the world. Integrated pest management (IPM) involves choosing appropriate tactics from a range of pest control techniques including biological, cultural, and chemical methods to suit individual cropping systems, pest complexes, and local environments [1,2,3,4]. It has been proved both theoretically [2, 5] and experimentally [6, 7] that IPM has been more effective than the biological control or chemical control alone. Based on the above factors, we propose a generalized mathematical model with nonlinear pulse control tactics in order to investigate the effect of limited resources on the outbreak of pest populations. The paper ends with some interesting biological conclusions and numerical bifurcation analyses, which complement the theoretical findings
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