Mathematical Study of Hybrid Impulsive Pest Control Model with Stage Structuring

2018 ◽  
Vol 85 (3-4) ◽  
pp. 265
Author(s):  
Bhanu Gupta ◽  
Amit Sharma ◽  
Sanjay K. Srivastava
Keyword(s):  
Pest Control ◽  
Natural Enemies ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Hybrid Approach ◽  
Control Model ◽  
Point Of View ◽  
Impulsive Effect ◽  
Mature Adult ◽  
The Rich

It is a need of time to use hybrid approach (biological and chemical) to control agriculture pests effectively, economically and safely. Most of the pests and natural enemies in their life history goes through two stages namely immature larva and mature adult. From this biological point of view, we purpose a pest control model with stage structuring in pests and natural enemies in the presence of impulsively released natural enemy and chemical pesticides. Using Floquet theory and small ampli- tude perturbation technique, the local stability of periodic solutions are discussed. The suffcient conditions for the global attractively of pest- extinction periodic solution and permanence of the system are obtained by using comparison technique of differential equations with impulsive effect. At last an extensive simulation is done to verify the theoretical ndings and to see the rich dynamical behavior of the system.

scholarly journals Dynamics of a Stage Structure Pest Control Model with Impulsive Effects at Different Fixed Time

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Bing Liu ◽  
Ying Duan ◽  
Yinghui Gao
Keyword(s):  
Time Delay ◽  
Pest Control ◽  
Natural Enemies ◽  
Stage Structure ◽  
Threshold Level ◽  
Fixed Time ◽  
Control Model ◽  
Pest Population ◽  
Maturation Time ◽  
Maturation Time Delay

Many existing pest control models, which control pests by releasing natural enemies, neglect the effect that natural enemies may get killed. From this point of view, we formulate a pest control model with stage structure for the pest with constant maturation time delay (through-stage time delay) and periodic releasing natural enemies and natural enemies killed at different fixed time and perform a systematic mathematical and ecological study. By using the comparison theorem and analysis method, we obtain the conditions for the global attractivity of the pest-eradication periodic solution and permanence of the system. We also present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is uniformly permanent. We show that maturation time delay, impulsive releasing, and killing natural enemies can bring great effects on the dynamics of the system. Numerical simulations confirm our theoretical results.

A pest control model with state-dependent impulses

2015 ◽  
Vol 08 (01) ◽  
pp. 1550009 ◽  
Author(s):  
Xuehui Ji ◽  
Sanling Yuan ◽  
Lansun Chen
Keyword(s):  
Periodic Solution ◽  
Pest Control ◽  
Control Model ◽  
Point Of View ◽  
Successor Function ◽  
Pest Population ◽  
Single Measure ◽  
State Dependent ◽  
Two Measures ◽  
Order One Periodic Solution

In this paper, a pest control model with state-dependent impulses is firstly established, which relies on releasing of natural enemies, together with spraying pesticides. By using the successor function of differential equation geometry rules, the existence of order one periodic solution is discussed. According to the Analogue of Poincaré's Criterion, the orbitally asymptotic stability of the order one periodic solution is obtained. Furthermore, we investigated the global attractor of the system. From a biological point of view, our results indicate that: (1) the pest population can be controlled below some threshold; (2) compared to single measure, it is more efficient to take two measures for reducing the level of the pests.

scholarly journals Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bing Liu ◽  
Ling Xu ◽  
Baolin Kang
Keyword(s):  
Pest Control ◽  
Natural Enemies ◽  
Natural Enemy ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Control Model ◽  
Polluted Environment ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. We assume only that the natural enemies are affected by pollution, and we choose the method to kill the pest without harming natural enemies. Sufficient conditions for global attractivity of the natural enemy-extinction periodic solution and permanence of the system are obtained. Numerical simulations are presented to confirm our theoretical results.

scholarly journals Stability Analysis of Integrated Pest Management with Impulsive Biological Control

2018 ◽  
Vol 6 (2) ◽  
pp. 79-91
Author(s):  
Bhanu Gupta ◽  
Amit Sharma ◽  
Sanjay K. Srivastava
Keyword(s):  
Biological Control ◽  
Periodic Solution ◽  
Natural Enemies ◽  
Local Stability ◽  
Small Amplitude ◽  
Global Attractivity ◽  
Perturbation Technique ◽  
Impulsive Differential Equations ◽  
Control Model ◽  
Sufficient Condition

The aim of the present work is to study the dynamics of stage-structured pest control model including biological control, i.e. by releasing of natural enemies and infected pests periodically. It is assumed that only immature susceptible pests are attacked by natural enemies admitting Beddington DeAngelis functional response and mature susceptible pests are contacted by infected pests with bilinear incidence rate and become exposed. The sufficient condition for local stability of pest extinction periodic solution is derived by making use of Floquet’s theory and small amplitude perturbation technique. The global attractivity of pest extinction periodic solution is also established by applying comparison principle of impulsive differential equations.

Dynamics Analysis of a Filippov Pest Control Model with Time Delay

2021 ◽  
pp. 105865
Author(s):  
Ayman A. Arafa ◽  
Soliman A.A. Hamdallah ◽  
Sanyi Tang ◽  
Yong Xu ◽  
Gamal M. Mahmoud
Keyword(s):  
Time Delay ◽  
Pest Control ◽  
Control Model ◽  
Dynamics Analysis

scholarly journals Intercropping Rosemary (Rosmarinus officinalis) with Sweet Pepper (Capsicum annum) Reduces Major Pest Population Densities without Impacting Natural Enemy Populations

Insects ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 74
Author(s):  
Xiao-wei Li ◽  
Xin-xin Lu ◽  
Zhi-jun Zhang ◽  
Jun Huang ◽  
Jin-ming Zhang ◽  
...  
Keyword(s):  
Integrated Pest Management ◽  
Pest Management ◽  
Pest Control ◽  
Natural Enemies ◽  
Natural Enemy ◽  
Sweet Pepper ◽  
Population Densities ◽  
Pest Population ◽  
Major Pest ◽  
Population Suppression

Intercropping of aromatic plants provides an environmentally benign route to reducing pest damage in agroecosystems. However, the effect of intercropping on natural enemies, another element which may be vital to the success of an integrated pest management approach, varies in different intercropping systems. Rosemary, Rosmarinus officinalis L. (Lamiaceae), has been reported to be repellent to many insect species. In this study, the impact of sweet pepper/rosemary intercropping on pest population suppression was evaluated under greenhouse conditions and the effect of rosemary intercropping on natural enemy population dynamics was investigated. The results showed that intercropping rosemary with sweet pepper significantly reduced the population densities of three major pest species on sweet pepper, Frankliniella intonsa, Myzus persicae, and Bemisia tabaci, but did not affect the population densities of their natural enemies, the predatory bug, Orius sauteri, or parasitoid, Encarsia formosa. Significant pest population suppression with no adverse effect on released natural enemy populations in the sweet pepper/rosemary intercropping system suggests this could be an approach for integrated pest management of greenhouse-cultivated sweet pepper. Our results highlight the potential of the integration of alternative pest control strategies to optimize sustainable pest control.

The Control of the Eye's Intrinsic Muscles: A Multivariable Optimum Performance Control System

1968 ◽  
Vol 1 (8) ◽  
pp. T.129-T.132 ◽  
Author(s):  
F. M. Toates
Keyword(s):  
Control System ◽  
Control Systems ◽  
Pupil Diameter ◽  
Control Model ◽  
Point Of View ◽  
Theoretical Point ◽  
Pupil Control ◽  
Performance Control ◽  
A Value ◽  
Intrinsic Muscles

The reciprocal interaction between the accommodation and pupil control systems of the human eye is examined from a theoretical point of view. The system, which is responsible for maintaining pupil diameter at a value which is a compromise between conflicting requirements, is represented by a control model, and is considered in terms of the concept of a performance index.

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