Hybrid approach for pest control with impulsive releasing of natural enemies and chemical pesticides: A plant–pest–natural enemy model

Jatav, Kunwer Singh; Dhar, Joydip

doi:10.1016/j.nahs.2013.11.011

Cited by 22 publications

(9 citation statements)

References 23 publications

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“…T is a solution of system (2). Since condition (H2) holds, similar to the proofs of Lemma 31 and Theorem 79 in [18], we can also prove that (x(t), y(t), z(t)) T is almost periodic.…”

supporting

confidence: 57%

“…, then there exists an unique almost periodic solution which is uniformly asymptotically stable for the almost periodic system (2).…”

Section: Resultsmentioning

confidence: 99%

“…As the dynamics in the agricultural ecological system is concerned, the specie of crops, the pests and the enemies constitute a food-chain system, and the artificial insecticides irregularly decreasing the number of species can be described by impulsive perturbations on the food-chain system; see [1][2][3][4] etc.…”

Section: Introductionmentioning

confidence: 99%

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A non-autonomous impulsive food-chain model with delays

Tian

Zhang

et al. 2019

Adv Differ Equ

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A non-autonomous almost periodic prey-predator system with impulsive effects and multiple delays is proposed in this paper, Holling's type-IV systems and ratio-dependent functional responses are also involved in the model. By applying absolute inequalities, integral inequalities, differential inequalities and the mean-value theorem and other mathematical analysis techniques, we obtain some sufficient conditions which guarantee the permanence of the system. Moreover, we obtain the existence and the uniqueness of the almost periodic solution which is uniformly asymptotically stable by constructing a series of Lyapunov functionals. Finally, we present several numerical examples to verify the theoretical results and present some discussions of pest management in the agricultural ecological system.

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“…T is a solution of system (2). Since condition (H2) holds, similar to the proofs of Lemma 31 and Theorem 79 in [18], we can also prove that (x(t), y(t), z(t)) T is almost periodic.…”

supporting

confidence: 57%

“…, then there exists an unique almost periodic solution which is uniformly asymptotically stable for the almost periodic system (2).…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

A non-autonomous impulsive food-chain model with delays

Tian

Zhang

et al. 2019

Adv Differ Equ

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“…As was pointed out, several authors have contributed to the theoretical analysis of those systems, with particular emphasis on the existence and stability of pest-free solutions, as well as finding explicit thresholds for control parameters at which stability is lost (bifurcations). While this is generally a straightforward task for models belonging to the class of smooth ordinary differential equations, the situation can be more involved for other types of systems, for example, impulsive differential equations; see [43,44,48,55,56]. Although impulsive systems describing pest control methods have received a good deal of attention in the past, numerical investigations of such models are rather scarce in the literature and are mostly carried out at the simulation level.…”

Section: Numerical Analysis Of a Pest Control Scheme With Impulsive Ementioning

confidence: 99%

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

Chávez

Jungmann

Siegmund

2017

International Journal of Differential Equations

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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.

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“…With the development of agriculture science and technology, a variety of pest control methods are available, such as chemical control, biological control, physical control and remote sensing [1]. Chemical and biological controls have been studied by many researchers, especially for two species predator-prey system or three-specie food chain system [2][3][4].…”

Section: Introductionmentioning

confidence: 99%