scholarly journals Multi-State Dependent Impulsive Control for Pest Management

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Huidong Cheng ◽  
Fang Wang ◽  
Tongqian Zhang
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Qualitative Analysis ◽  
Pest Management ◽  
Pest Control ◽  
Impulsive Control ◽  
Management Strategies ◽  
Control Methods ◽  
State Dependent ◽  
Order One Periodic Solution

According to the integrated pest management strategies, we propose a model for pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution of such system, and further, the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results. Our results show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.

scholarly journals Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Huidong Cheng ◽  
Fang Wang ◽  
Tongqian Zhang
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Chemical Control ◽  
Impulsive Control ◽  
Control Methods ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
State Dependent ◽  
Order One Periodic Solution

According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.

scholarly journals Existence and Attractiveness of Order One Periodic Solution of a Holling I Predator-Prey Model

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Huidong Cheng ◽  
Tongqian Zhang ◽  
Fang Wang
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Impulsive Control ◽  
Management Strategies ◽  
Type I ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
State Dependent ◽  
Order One Periodic Solution

According to the integrated pest management strategies, a Holling type I functional response predator-prey system concerning state-dependent impulsive control is investigated. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution, and the attractivity of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient than the existing ones for proving the existence and attractiveness of order one periodic solution.

scholarly journals Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Changtong Li ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Pest Control ◽  
Impulsive Control ◽  
Period Doubling ◽  
Dynamical Behaviour ◽  
Period Doubling Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model

Abstract An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed and its dynamics is investigated. The threshold conditions for the global stability of the pest-free periodic solution are obtained based on the Floquet theorem and analytic methods. Also, the sufficient conditions for permanence are given. Additionally, the problem of finding a nontrivial periodic solution is confirmed by showing the existence of a nontrivial fixed point of the model’s stroboscopic map determined by a time snapshot equal to the common impulsive period. In order to address the effects of nonlinear pulse control on the dynamics and success of pest control, a predator–prey model incorporating the Holling type II functional response function as an example is investigated. Finally, numerical simulations show that the proposed model has very complex dynamical behaviour, including period-doubling bifurcation, chaotic solutions, chaos crisis, period-halving bifurcations and periodic windows. Moreover, there exists an interesting phenomenon whereby period-doubling bifurcation and period-halving bifurcation always coexist when nonlinear impulsive controls are adopted, which makes the dynamical behaviour of the model more complicated, resulting in difficulties when designing successful pest control strategies.

IMPULSIVE CONTROL STRATEGIES FOR PEST MANAGEMENT

2007 ◽  
Vol 15 (02) ◽  
pp. 235-260 ◽  
Author(s):  
HONG ZHANG ◽  
LANSUN CHEN ◽  
PAUL GEORGESCU
Keyword(s):  
Periodic Solution ◽  
Pest Management ◽  
Impulsive Control ◽  
Control Strategies ◽  
Integrated Management ◽  
Management Strategies ◽  
Critical Value ◽  
Globally Asymptotically Stable ◽  
Pest Eradication ◽  
Low Levels

In this paper, we propose two impulsive differential systems concerning biological and, respectively, integrated pest management strategies. In each case, it is observed that there exists a globally asymptotically stable susceptible pest-eradication periodic solution on condition that the amount of infective pests released periodically is larger than a certain critical value. When the amount of infective pests released is less than this critical value, the system is shown to be permanent, which implies that the trivial susceptible pest-eradication solution loses its stability. Further, the existence of a non-trivial periodic solution is also studied by means of numerical simulations. In the case in which a single control is used, one can only use the amount of infective pests which are periodically released in order to control pests at desirable low levels, while in the case in which integrated management is used, one can use the proportion of pests removed by means of spraying chemical pesticides together with the amount of infective pests which are periodically released to control pests at desirable low levels.

scholarly journals Complex Dynamics of Beddington–DeAngelis-Type Predator-Prey Model with Nonlinear Impulsive Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Changtong Li ◽  
Xiaozhou Feng ◽  
Yuzhen Wang ◽  
Xiaomin Wang
Keyword(s):  
Periodic Solution ◽  
Pest Management ◽  
Pest Control ◽  
Natural Enemy ◽  
Complex Dynamics ◽  
Impulsive Control ◽  
Control Strategies ◽  
Resource Limitation ◽  
Predator Prey ◽  
Predator Prey Model

According to resource limitation, a more realistic pest management is that the impulsive control actions should be adjusted according to the densities of both pest and natural enemy in the field, which result in nonlinear impulsive control. Therefore, we have proposed a Beddington–DeAngelis interference predator-prey model concerning integrated pest management with both density-dependent pest and natural enemy population. We find that the pest-eradication periodic solution is globally stable if the impulsive period is less than the critical value by Floquet theorem. The condition of permanent is established, and a stable positive periodic solution appears via a supercritical bifurcation by bifurcation theorem. Finally, in order to investigate the effects of those nonlinear control strategies on the successful pest control, the bifurcation diagrams showed that the model exists with very complex dynamics. Consequently, the resource limitation may result in pest outbreak in complex ways, which means that the pest control strategies should be carefully designed.

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 A Holling Type II Pest and Natural Enemy Model with Density Dependent IPM Strategy

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Xia Wang ◽  
Yuan Tian ◽  
Sanyi Tang
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Pest Control ◽  
Natural Enemies ◽  
Natural Enemy ◽  
Impulsive Control ◽  
Control Measures ◽  
Threshold Condition ◽  
Density Dependent

Resource limitations and density dependent releasing of natural enemies during the pest control and integrated pest management will undoubtedly result in nonlinear impulsive control. In order to investigate the effects of those nonlinear control strategies on the successful pest control, we have proposed a pest-natural enemy system concerning integrated pest management with density dependent instant killing rate and releasing rate. In particular, the releasing rate depicts how the number of natural enemy populations released was guided by their current density at the fixed moment. The threshold condition which ensures the existence and global stability of pest-free periodic solution has been discussed first, and the effects of key parameters on the threshold condition reveal that reducing the pulse period does not always benefit pest control; that is, frequent releasing of natural enemies may not be beneficial to the eradication of pests when the density dependent releasing method has been implemented. Moreover, the forward and backward bifurcations could occur once the pest-free periodic solution becomes unstable, and the system could exist with very complex dynamics. All those results confirm that the control actions should be carefully designed once the nonlinear impulsive control measures have been taken for pest management.

scholarly journals Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Zhenzhen Shi ◽  
Qingjian Li ◽  
Weiming Li ◽  
Huidong Cheng
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Poincaré Map ◽  
Global Dynamics ◽  
Poincare Map ◽  
Existence And Stability ◽  
Sufficient And Necessary Conditions ◽  
Predator Model ◽  
Order One Periodic Solution

An integrated pest management prey-predator model with ratio-dependent and impulsive feedback control is investigated in this paper. Firstly, we determine the Poincaré map which is defined on the phase set and discuss its main properties including monotonicity, continuity, and discontinuity. Secondly, the existence and stability of the boundary order-one periodic solution are proved by the method of Poincaré map. According to the Poincaré map and related differential equation theory, the conditions of the existence and global stability of the order-one periodic solution are obtained when ΦyA<yA, and we prove the sufficient and necessary conditions for the global asymptotic stability of the order-one periodic solution when ΦyA>yA. Furthermore, we prove the existence of the order-kk≥2 periodic solution under certain conditions. Finally, we verify the main results by numerical simulation.

scholarly journals The Promise of a Multi-Disciplinary, Mixed-Methods Approach to Inform Insect Pest Management: Evidence From Wyoming Alfalfa

2020 ◽  
Vol 4 ◽  
Author(s):  
Randa Jabbour ◽  
Shiri Noy
Keyword(s):  
Mixed Methods ◽  
Focus Groups ◽  
Pest Management ◽  
Pest Control ◽  
Cropping Systems ◽  
Insect Pest ◽  
Management Strategies ◽  
Insect Pest Management ◽  
Biological Pest Control ◽  
Insect Management

Pest management strategies involve a complex set of considerations, circumstances, and decision-making. Existing research suggests that farmers are reflexive and reflective in their management choices yet continue to employ curative rather than preventative strategies, and opt for chemical over biological solutions. In this piece, we detail work from a two-year, multidisciplinary, mixed-methods study of insect pest management strategies in alfalfa in Wyoming, integrating data from four focus groups, a statewide survey, and biological sampling of production fields. We outline how these different sources of data together contribute to a more complete understanding of the challenges and strategies employed by farmers, and specifically on biological pest control. We applied this approach across alfalfa hay and seed crop systems. Relatively few farmers acknowledged biological control in focus groups or surveys, yet biological exploration yielded abundant parasitism of common pest alfalfa weevil. On the other hand, parasitism of seed alfalfa pest Lygus was far less common and patchy across fields. It is only in integrating quantitative and qualitative, biological and social data that we are able to generate a more complete portrait of the challenges and opportunities of working with farmers to embrace a preventative paradigm. In doing so, we offer insights on possible barriers to the adoption of preventative insect management strategies and provide a case study of integrating social science and biophysical techniques to better understand opportunities to expand biological pest control in cropping systems.

DYNAMICS ON A HOLLING II PREDATOR–PREY MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

2012 ◽  
Vol 05 (03) ◽  
pp. 1260006 ◽  
Author(s):  
BING LIU ◽  
YE TIAN ◽  
BAOLIN KANG
Keyword(s):  
Periodic Solution ◽  
Chemical Control ◽  
Impulsive Control ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
State Dependent ◽  
Continuous Dynamic System ◽  
Continuous Dynamic ◽  
Holling Ii Functional Response

According to biological and chemical control strategy for pest control, a Holling II functional response predator–prey system concerning state-dependent impulsive control is investigated. We define the successor functions of semi-continuous dynamic system and give an existence theorem of order 1 periodic solution of such a system. By means of sequence convergence rules and qualitative analysis, we successfully get the conditions of existence and attractiveness of order 1 periodic solution. Our results show that our method used in this paper is more efficient and easier than the existing methods to prove the existence and attractiveness of order 1 periodic solution.

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