THE DYNAMICAL BEHAVIOR OF NON-SMOOTH SYSTEM WITH IMPULSIVE CONTROL STRATEGIES

2012 ◽  
Vol 05 (03) ◽  
pp. 1260018 ◽  
Author(s):  
YUAN-SHUN TAN ◽  
JU-HUA LIANG ◽  
SAN-YI TANG
Keyword(s):  
Impulsive Control ◽  
Control Strategies ◽  
Dynamical Behavior ◽  
Economic Injury Level ◽  
Economic Threshold ◽  
Pest Population ◽  
Different Types ◽  
Economic Injury ◽  
The Given ◽  
Smooth System

Non-smooth system including impulsive strategies at both fixed and unfixed times are analyzed. For the model with fixed impulsive effects, the global stability of pest eradication periodic solution and the dominance of dynamic behavior are investigated. This indicates that the model with fixed moments has the potential to protect the natural enemies from extinction, but under some conditions may also serve to extinction of the pest. The second model is constructed according to the practices of IPM, that is, when the pest population reaches the economic injury level, a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is used. Numerical investigations imply that there are several different types of periodic solutions and their maximum amplitudes are always less than the given economic threshold. The results also show that the time series at which the IPM strategies are applied are quite complex, which means that the application and realization of IPM in practice are very difficult.

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 Threshold Strategy for Nonsmooth Filippov Stage-Structured Pest Growth Models

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Fengmei Tao ◽  
Baolin Kang ◽  
Bing Liu ◽  
Leilei Qu
Keyword(s):  
Sliding Mode ◽  
Growth Models ◽  
Control Strategies ◽  
Threshold Strategy ◽  
Economic Threshold ◽  
Pest Population ◽  
Threshold Policy ◽  
System A ◽  
Local Bifurcations ◽  
Nonsmooth Dynamical System

In order to control pests and eventually maintain the number of pests below the economic threshold, in this paper, based on the nonsmooth dynamical system, a two-stage-structured pest control Filippov model is proposed. We take the total number of juvenile and adult pest population as the control index to determine whether or not to implement chemical control strategies. The sliding-mode domain and conditions for the existence of regular and virtual equilibria, pseudoequilibrium, boundary equilibria, and tangent points are given. Further, the sufficient condition of the locally asymptotic stability of pseudoequilibrium is obtained. By numerical simulations, the local bifurcations of the equilibria are discussed. Our results show that the total number of pest populations can be successfully controlled below the economic threshold by taking suitable threshold policy.

Life table and economic threshold concept for ecologically sustainable management of Diacrisia casignetum Kollar (Lepidoptera: Arctiidae) on Jute

ENTOMON ◽  
2019 ◽  
Vol 44 (2) ◽  
pp. 103-110
Author(s):  
Nayan Roy
Keyword(s):  
Life Table ◽  
Demographic Data ◽  
Intrinsic Rate ◽  
Natural Increase ◽  
Economic Injury Level ◽  
Economic Threshold ◽  
Potential Fecundity ◽  
Rate Of Increase ◽  
Economic Injury ◽  
Ecologically Sustainable

Life table and economic threshold (ET) level of Diacrisia casignetum Kollar on jute was calculated in West Bengal condition during 2016-2018 for environmentally benign management and better production of jute. The demographic data of D. casignetum always construct type-III survivorship curve like most of the insects. Potential fecundity (Pf) and total fertility rate (Fx) were 384.667±5.487 and 30893.60±1063.586, respectively. The average intrinsic rate of natural increase (rm) and the daily finite rate of increase (ë) were 0.106±0.001 and 1.111±0.003 respectively with the generation time (Tc) of 41.520±0.069 and doubling time (DT) of 6.563±0.021 days. Their mean population momentum factor of increase (PMF) was 19.676±0.605 including vital index (VI) and trend index (TI) of 0.522±0.003 and 92.359±2.648, respectively with different levels of significance. The economic injury level (EIL) and ET based on percent yield loss of jute were 7.119±2.166 and 6.385±1.969 pests per plant, respectively. At single pest observation per plant, the possible time taken to reach EIL (Ti) and ET (Tt) were 6.377±3.292 and 5.377±3.292 days, respectively which will be useful for better cultivation of jute and other subsequent crops.

scholarly journals Sequential sampling plan, yield loss components and economic thresholds for the pepper weevil, Anthonomus eugenii Cano (Coleoptera: Curculionidae)

1969 ◽  
Vol 72 (3) ◽  
pp. 375-385
Author(s):  
Alejandro E. Segarra-Carmona ◽  
Alberto Pantoja
Keyword(s):  
Yield Loss ◽  
Negative Binomial ◽  
Control Strategies ◽  
Sequential Sampling ◽  
Weekly Schedule ◽  
Economic Injury Level ◽  
Economic Thresholds ◽  
Density Relationship ◽  
Economic Injury ◽  
Pepper Weevil

A negative binomial distribution best predicted pepper weevil spatial dispersion on pepper plants. Sequential sampling plans for economic threshold (ET) levels of 0.1 and 0.5 adult weevils per plant were developed and tested against a weekly schedule of sprayed and unsprayed check treatments in mini-plots. Weekly sprayed and 0.1 ET mini-plots had similar yield, but higher than 0.5 ET or mini-plots never sprayed. Direct cost to farmers was the same either with 0.1 ET or weekly sprays. However, insecticide applications were reduced by one-third with 0.1 ET. Fruit abortion constituted the main yield-loss component in the pepper weevil-pepper system. An empirical yield-loss vs. adult weevil population density relationship was estimated. This estimate agreed with a theoretical economic injury level of 0.01 adult per plant. Recommendations on the use of prophylactic and responsive control strategies for the pepper weevil are given.

scholarly journals Economic Injury Level of Canjiqueira in Native Pastures in Pantanal of Nhecolândia

2019 ◽  
Vol 37 ◽  
Author(s):  
C. BERSELI ◽  
J.A.M. BONO ◽  
S.A. SANTOS ◽  
F.A.R. PEREIRA ◽  
J.F. REIS NETO
Keyword(s):  
Threshold Level ◽  
Human Intervention ◽  
Effective Management ◽  
Economic Injury Level ◽  
Economic Threshold ◽  
Shrub Species ◽  
Invasive Shrub ◽  
Economic Injury ◽  
Native Pastures ◽  
Livestock System

ABSTRACT: Pantanal plain has large extensions of land formed by many types of landscapes suitable to extensive livestock system. Open grasslands and lowlands are formed by forage such as grasses and forbs widely consumed by cattle. However, climatic and human factors can promote the dissemination of invasive shrub species such as canjiqueira (Byrsonima cydoniifolia A. Juss) making it necessary, in many cases, the human intervention to control the invasion. The present work had as objective to determine the economic threshold level to control canjiqueira through two methods: tractor driven blade and link chains pulled by tractor in different invasion levels plants per hectare. Economic Threshold proved to be a tool for efficient and effective management for making decisions of when and how to do the control of canjiqueira in natural pastures of Pantanal of Nhecolândia.

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>

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