Oscillation in Pest Population and Its Management: A Mathematical Study
11 Feb 2013-International Journal of Mathematics and Mathematical Sciences (Hindawi)-Vol. 2013, Iss: 2013, pp 1-12
TL;DR: By the Hopf bifurcation theory, the existence of the stable oscillation of the system is proved and the improved version of PMP is applied to perform the optimal analysis of the pest control model as a special case.
Abstract: We study the role of predation dynamics in oscillation of pest population in insect ecology. A two-dimensional pest control model (under the use of insecticides) with time delay in predation is considered in this paper. By the Hopf bifurcation theory, we prove the existence of the stable oscillation of the system. We also consider the economic viability of the control process. First we improve the Pontryagin maximum principle (PMP) where the delay in the system is sufficiently small and control function is linear, and then we apply the improved version of PMP to perform the optimal analysis of the pest control model as a special case.
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TL;DR: In this paper, the Third Edition of the Third edition of Linear Systems: Local Theory and Nonlinear Systems: Global Theory (LTLT) is presented, along with an extended version of the second edition.
Abstract: Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index
1,685 citations
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TL;DR: The results show that schematic implementation of complex pesticide control and biological control measures to reduce the harm brought by pests to crops will have significant implications in agriculture research.
Abstract: . In agricultural management and ecological research, consideration of the impacts and risks of pests on the dynamics of crop growth has been introduced in the literature using process-based models at different ecological levels with varied usefulness. In this study, we attempt to overcome the selected limitations of some existing process-based models while (i) systematically developing coupled pest-crop systems, (ii) evaluating the results under the application of various types of interventions, and (iii) comparing the analysis with similar studies in the literature. The novelty of the paper lies in the consideration of a continuous system with discrete-time treatments. In particular, we have established the long-term behavior of two modeling frameworks capturing the growth of the crop infested with a different type of pests and different pesticide application strategies to control the exponentially growing pest population. In the first pesticide application strategy, pesticides are sprayed at fixed time intervals whereas, under the second strategy, pesticides are implemented when the pest population reaches Economic Threshold (ET) in pest abundance. Conditions on critical pest population size when single treatment and multiple treatments of pesticides in both the modeling frameworks have been discussed. The optimal timing of pesticide implementation, the optimal dosage of pesticide, the economic threshold of pests, and the threshold of pest survival rate have been obtained (both mathematically and numerically) to maximize the profit Further, we have also extended the model and the exponentially growing pest population is optimized by biological control linear feedback control to reduce the pest population to a desired economic threshold value. The numerical analysis validating analytical results is discussed for both the cases of chemical and biological control. Finally, using the sensitivity analysis technique, sensitive model parameters affecting the optimal dosage, optimal time, and optimal survival rate are identified in the case of chemical control. The results show that schematic implementation of complex pesticide control and biological control measures to reduce the harm brought by pests to crops will have significant implications in agriculture research.
References
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Book•
[...]
TL;DR: In this paper, the Third Edition of the Third edition of Linear Systems: Local Theory and Nonlinear Systems: Global Theory (LTLT) is presented, along with an extended version of the second edition.
Abstract: Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index
1,685 citations
"Oscillation in Pest Population and ..." refers methods in this paper
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01 Aug 1958
TL;DR: The present data indicate that if an adequate environment is encompassed, the predator-prey relation is not necessarily self-annihilative, and that absolutely restrictive refuges are not essential, and the view that more stable control of a population is likely to result in an environment of balanced heterogeneity than in one of simpler structure.
Abstract: Experimental studies on the role of dispersion in predator-prey relations was studied
under controlled laboratory conditions using the phytophagous mite Eotetranychus sexmaculatus as prey, and the mite Typhlodromus occidentalis as predator. The results are a beginning toward answering some of the theoretical
questions presented to population ecologists.
The present data indicate that if an adequate environment is encompassed, the predator-prey
relation is not necessarily self-annihilative, and that absolutely restrictive refuges
are not essential. The results also support the view that more stable control of a
population is likely to result in an environment of balanced heterogeneity than in
one of simpler structure.
In this study a predator-prey relation was maintained for three successive oscillation
waves before overexploitation finally ended the relation in the most complex universe
or ecosystem utilized.
Some of the questions which may ultimately be answered by such studies include: Are such oscillations inherently of increasing amplitude?
If so, are there commonly present forces which act to cancel this tendency?
Does the presence of other significant species in addition to the two original coactors
tend to stabilize or disturb the relation?
What may be the effect of changes in the physical conditions upon the degree of stability
or permanence of the relation?
Can evidence be obtained regarding the concept that the prey, as well as the predator,
may benefit from the relation?
What is the order of influence on stability of such factors as shelter, food, disease,
and natural enemies of other kinds?
1,234 citations
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TL;DR: It is shown that trapping figures for the lynx are definitely related to weather conditions, and the significance of this for the various theories of the origin and synchronization of the cycle is discussed.
Abstract: It is shown that trapping figures for the lynx are definitely related to weather conditions. The significance of this for the various theories of the origin and synchronization of the cycle is discussed.
868 citations
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742 citations
"Oscillation in Pest Population and ..." refers methods in this paper
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