A Pest Management Model with Stage Structure and Impulsive State Feedback Control

Guoping Pang,Weijian Xu,Gang Fu,Zhiqing Liang,Lijie Li

doi:10.1155/2015/617379

Abstract

A pest management model with stage structure and impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 periodic solution of the semicontinuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of Poincarè criterion. Finally, we analyze numerically the theoretical results obtained.

Highlights

Banana leaves diseases are divided into epiphyte and virus
Nymphs transmit virus to healthy plants only through short-distance crawling since genitalia and wings of nymphs are not fully developed yet, and infected nymphs have slight infective power
After 4 instars, nymphs grow into adults which have fully developed genitalia and wings and can oviposit and transmit virus to healthy plants through migrating after piercing and sucking the virus of diseased plants, so infected adults have strong infective power

Summary

Introduction

Banana leaves diseases are divided into epiphyte and virus. Banana bunchy top disease (i.e., Prawn banana, Green banana, Banana) is one of virus diseases, caused by Banana bunchy top virus. The development of banana aphids includes three stages: egg, nymph, and adult (winged form). Once pest density rises to ET, some measures must be carried out to prevent EIL (economic injure tolerate level) from happening To control pests, such a measure for spraying pesticides is always adopted when pest density arrives at a given ET. For impulsive state feedback control systems, the sufficient condition for the existence and the orbitally asymptotically stability of the order-1 periodic solutions have been obtained by differential equation geometry theory, the method of successor function, and analog of Poincarecriterion [5,6,7,8,9,10,11,12,13,14].

Preliminaries

Existence of the Order-1 Periodic Solution

Stability of the Order-1 Periodic Solution

Numerical Analysis and Discussion