scholarly journals Two Generalized Predator-Prey Models for Integrated Pest Management with Stage Structure and Disease in the Prey Population

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Ruiqing Shi ◽  
Sanyi Tang ◽  
Wenli Feng
Keyword(s):  
Integrated Pest Management ◽  
Pest Management ◽  
Natural Enemies ◽  
Impulsive Control ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Predator Prey ◽  
Predator Prey Models ◽  
Impulsive Release

Stage-structured predator-prey models with disease in the prey are constructed. For the purpose of integrated pest management, two types of impulsive control strategies (impulsive release of infective prey and impulsive release of predator) are used. For Case  1, infective prey applications are more frequent than releases of predator (natural enemies). For Case  2, predator (natural enemies) releases are more frequent than infective prey applications. In both cases, we get the sufficient conditions for the global attractivity of the susceptible prey-eradication periodic solution. In addition, the persistence of the systems is also discussed. At last, the results are discussed and some possible future work is put forward.

scholarly journals Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control

2021 ◽  
Vol 18 (6) ◽  
pp. 7318-7343
Author(s):  
Yuan Tian ◽  
◽  
Sanyi Tang ◽  
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Natural Enemies ◽  
Impulsive Control ◽  
Control Strategies ◽  
Integrated Management ◽  
Rapid Development ◽  
Dynamical Behavior ◽  
Density Dependent

<abstract><p>Spraying insecticides and releasing natural enemies are two commonly used methods in the integrated pest management strategy. With the rapid development of biotechnology, more and more realistic factors have been considered in the establishment and implementation of the integrated pest management models, such as the limited resources, the mutual restriction between pests and natural enemies, and the monitoring data of agricultural insects. Given these realities, we have proposed a pest-natural enemy integrated management system, which is a nonlinear state-dependent feedback control model. Besides the anti-predator behavior of the pests to the natural enemies is considered, the density dependent killing rate of pests and releasing amount of natural enemies are also introduced into the system. We address the impulsive sets and phase sets of the system in different cases, and the analytic expression of the Poincaré map which is defined in the phase set was investigated. Further we analyze the existence, uniqueness, global stability of order-1 periodic solution. In addition, the existence of periodic solution of order-$ k $ ($ k\geq2 $) is discussed. The theoretical analyses developed here not only show the relationship between the economic threshold and the other key factors related to pest control, but also reveal the complex dynamical behavior induced by the nonlinear impulsive control strategies.</p></abstract>

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.

AN INTEGRATED PEST MANAGEMENT MODEL WITH DOSE-RESPONSE EFFECT OF PESTICIDES

2018 ◽  
Vol 26 (01) ◽  
pp. 59-86 ◽  
Author(s):  
BAOLIN KANG ◽  
BING LIU ◽  
FENGMEI TAO
Keyword(s):  
Asymptotic Stability ◽  
Pest Management ◽  
Natural Enemies ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
Residual Effects ◽  
Delayed Response ◽  
Threshold Condition ◽  
Significant Control ◽  
Dose Response Effect

Considering the delayed response to pesticide applications and the long-term residual effects of pesticides after the deployment of a pest management strategy, this paper develops a pollutant-discharge model to simulate pesticide spraying and analyze the effect of releasing natural enemies of the pest. The following two different control strategies are discussed: (1) the frequency of spraying pesticides is higher than that of releasing natural enemies, and (2) the frequency of releasing natural enemies is higher than that of spraying pesticides. For different control strategies, the sufficient conditions of locally asymptotic stability and globally asymptotic stability of the pest-eradication periodic solution are obtained. Using numerical simulations, we analyze the sensitivity of the threshold condition with respect to the parameters, identify the major factors affecting pest control and provide guidance for decision-making in pest management. Finally, we compare the control strategies and analyze which strategy is optimal as the most significant control parameters are varying.

scholarly journals Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Min Zhao ◽  
Yanzhen Wang ◽  
Lansun Chen
Keyword(s):  
Integrated Pest Management ◽  
Pest Management ◽  
Control Strategy ◽  
Impulsive Control ◽  
Critical Parameters ◽  
Critical Conditions ◽  
Dynamic Complexity ◽  
Predator Prey ◽  
Impulsive Control Strategy ◽  
Disease In Prey

The dynamic behaviors of a predator-prey (pest) model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the local asymptotical stability and global attractivity for the semitrivial periodic solution and population persistent, which depicts the threshold expression of some critical parameters for carrying out integrated pest management. Numerical analysis indicates that the impulsive control strategy has a strong effect on the dynamical complexity and population persistent using bifurcation diagrams and power spectra diagrams. These results show that if the release amount of infective prey can satisfy some critical conditions, then all biological populations will coexist. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.

A NEW MATHEMATICAL MODEL FOR OPTIMAL CONTROL STRATEGIES OF INTEGRATED PEST MANAGEMENT

2007 ◽  
Vol 15 (02) ◽  
pp. 219-234 ◽  
Author(s):  
XINZHU MENG ◽  
ZHITAO SONG ◽  
LANSUN CHEN
Keyword(s):  
Periodic Solution ◽  
Control Problem ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Control Strategy ◽  
Impulsive Control ◽  
Control Strategies ◽  
Economic Damage ◽  
Pest Population ◽  
The Given

A state-dependent impulsive SI epidemic model for integrated pest management (IPM) is proposed and investigated. We shall examine an optimal impulsive control problem in the management of an epidemic to control a pest population. We introduce a small amount of pathogen into a pest population with the expectation that it will generate an epidemic and that it will subsequently be endemic such that the number of pests is no larger than the given economic threshold (ET), so that the pests cannot cause economic damage. This is the biological control strategy given in the present paper. The combination strategy of pulse capturing (susceptible individuals) and pulse releasing (infective individuals) is implemented in the model if the number of pests (susceptible) reaches the ET. Firstly, the impulsive control problem is to drive the pest population below a given pest level and to do so in a manner which minimizes a weighted sum of the cost of using the control. Hence, for a one time impulsive effect we obtain the optimal strategy in terms of total cost such that the number of pests is no larger than the given ET. Secondly, we show the existence of periodic solution with the number of pests no larger than ET, and by using the Analogue of the Poincaré Criterion we prove that it is asymptotically stable under a planned impulsive control strategy. Further, the period T of the periodic solution is calculated, which can be used to estimate how long the pest population will take to return back to its pre-control level. The main feature of the present paper is to apply an SI infectious disease model to IPM, and some pests control strategies are given.

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.

RATIO-DEPENDENT PREDATOR–PREY MODEL WITH STAGE STRUCTURE AND TIME DELAY

2012 ◽  
Vol 05 (04) ◽  
pp. 1250014 ◽  
Author(s):  
LIJUAN ZHA ◽  
JING-AN CUI ◽  
XUEYONG ZHOU
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent ◽  
Predator Prey Models

Ratio-dependent predator–prey models are favored by many animal ecologists recently as more suitable ones for predator–prey interactions where predation involves searching process. In this paper, a ratio-dependent predator–prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.

scholarly journals Dynamic Analysis of General Integrated Pest Management Model with Double Impulsive Control

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Yingke Li ◽  
Zhidong Teng ◽  
Kai Wang ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Threshold Value ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Globally Attractive

A general predator-prey model with disease in the prey and double impulsive control is proposed and investigated for the purpose of integrated pest management. By using the Floquet theory, the comparison theorem of impulsive differential equations, and the persistence theory of dynamical systems, we obtain that if threshold valueR0<1, then the susceptible pest eradication periodic solution is globally asymptotically stable and ifR0>1, then the model is permanent. The numerical examples not only illustrate the theoretical results, but also show that when the model is permanent, then it may possess a unique globally attractiveT-periodic solution.

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.

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