International Journal of Differential Equations

Modeling and Analysis of Integrated Pest Control Strategies via Impulsive Differential Equations

Joseph Páez Chávez, Dirk Jungmann, and Stefan Siegmund

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Abstract

The paper is concerned with the development and numerical analysis of mathematical models used to describe complex biological systems in the framework of Integrated Pest Management (IPM). Established in the late 1950s, IPM is a pest management paradigm that involves the combination of different pest control methods in ways that complement one another, so as to reduce excessive use of pesticides and minimize environmental impact. Since the introduction of the IPM concept, a rich set of mathematical models has emerged, and the present work discusses the development in this area in recent years. Furthermore, a comprehensive parametric study of an IPM-based impulsive control scheme is carried out via path-following techniques. The analysis addresses practical questions, such as how to determine the parameter values of the system yielding an optimal pest control, in terms of operation costs and environmental damage. The numerical study concludes with an exploration of the dynamical features of the impulsive model, which reveals the presence of codimension-1 bifurcations of limit cycles, hysteretic effects, and period-doubling cascades, which is a precursor to the onset of chaos.

Article information

Source
Int. J. Differ. Equ., Volume 2017, Special Issue (2017), Article ID 1820607, 18 pages.

Dates
Received: 2 August 2017
Accepted: 6 November 2017
First available in Project Euclid: 9 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1515467080

Digital Object Identifier
doi:10.1155/2017/1820607

Mathematical Reviews number (MathSciNet)
MR3737978

Zentralblatt MATH identifier
06915925

Citation

Páez Chávez, Joseph; Jungmann, Dirk; Siegmund, Stefan. Modeling and Analysis of Integrated Pest Control Strategies via Impulsive Differential Equations. Int. J. Differ. Equ. 2017, Special Issue (2017), Article ID 1820607, 18 pages. doi:10.1155/2017/1820607. https://projecteuclid.org/euclid.ijde/1515467080


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