Numerical Analysis of Discrete Switching Prey-Predator Model for Integrated Pest Management

Changcheng Xiang,Zhongyi Xiang,Yi Yang,Wenjie Qin

doi:10.1155/2016/8627613

Abstract

The switching discrete prey-predator model concerning integrated pest management has been proposed, and the switches are guided by the economic threshold (ET). To begin with, the regular and virtual equilibria of switching system have been discussed and the key parameter bifurcation diagrams for the existence of equilibria have been proposed, which reveal the three different regions of equilibria. Besides, numerical bifurcation analyses show that the switching discrete system may have complicated dynamics behavior including chaos and the coexistence of multiple attractors. Finally, the effects of key parameters on the switching frequencies and switching times are discussed and the sensitivity analysis of varying parameter values for mean switching times has also been given. The results proved that economic threshold (ET) and the growth rate (α) were the key parameters for pest control.

Highlights

The integrated pest management (IPM) is applied [1,2,3]
In model (3), if the prey stands for the pest population and the predator stands for the natural enemies, what we want to know is that how many key parameters affect the pest control when integrated pest management (IPM) is applied
We investigate the important parameters which affect mean switching times most significantly by using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCCs), including the reduction proportion of the pest population (p), the economic threshold (ET), the increasing proportion of natural enemies (τ), the conversion ratio (β), the growth rate (α), and death rate (δ)

Summary

Introduction

The integrated pest management (IPM) is applied [1,2,3]. IPM is a long-term control strategy that combines biological, cultural, and chemical tactics to reduce the density of pest populations to economic injury level (EIL) when the pests reach an economic threshold (ET) [1, 2]. In model (3), if the prey stands for the pest population and the predator stands for the natural enemies, what we want to know is that how many key parameters affect the pest control when integrated pest management (IPM) is applied. We want to discuss discrete-time prey-predator models by utilizing a threshold policy (TP) to control the pest population (prey). In the region G2, if the prey density is above ET in system (4), the IPM strategy is applied, which includes spraying the pesticides and releasing the natural enemies. Before we investigate the stability of the fixed point, we need the following lemma, which can be proved by the relations between roots and coefficients of a quadratic equation [5].

Fixed Point in Discrete Switching System

Numerical Bifurcation Analysis

Switching times 0

Discussion