Impulsive Ecological Control Of A Stage-Structured Pest Management System

Jiang, Guirong; Lu, QiShao; Peng, Linping

doi:10.3934/mbe.2005.2.329

Cited by 25 publications

(11 citation statements)

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“…Although this control measure is better than classical one, it has shortcomings, regardless of the growth rules of the prey pest and the cost of management. In recent years, in order to overcome such drawbacks, several researchers have started paying attention to another control measure based on the state feedback control strategy, which is taken only when the amount of the monitored prey pest population reaches a threshold value 2, [16][17][18][19] . Obviously, the latter control measure is more reasonable and suitable for prey pest control.…”

Section: Introductionmentioning

confidence: 99%

The Dynamics of a Predator‐Prey System with State‐Dependent Feedback Control

Baek

2012

Abstract and Applied Analysis

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A Lotka-Volterra-type predator-prey system with state-dependent feedback control is investigated in both theoretical and numerical ways. Using the Poincaré map and the analogue of the Poincaré criterion, the sufficient conditions for the existence and stability of semitrivial periodic solutions and positive periodic solutions are obtained. In addition, we show that there is no positive periodic solution with period greater than and equal to three under some conditions. The qualitative analysis shows that the positive period-one solution bifurcates from the semitrivial solution through a fold bifurcation. Numerical simulations to substantiate our theoretical results are provided. Also, the bifurcation diagrams of solutions are illustrated by using the Poincaré map, and it is shown that the chaotic solutions take place via a cascade of period-doubling bifurcations.

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Section: Introductionmentioning

confidence: 99%

The Dynamics of a Predator‐Prey System with State‐Dependent Feedback Control

Baek

2012

Abstract and Applied Analysis

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“…Now the common pest control strategies include chemical control (spraying pesticides) and biological control (releasing natural enemies). Many scholars [1][2][3][4][5][6][7][8][9][10] used mathematical models to simulate pest control strategies. Some of them [1][2][3][4] analyzed the dynamics of the pest control models based on biological control.…”

Section: Introductionmentioning

confidence: 99%

“…Some of them [1][2][3][4] analyzed the dynamics of the pest control models based on biological control. Whereas some studies [5][6][7][8][9][10] built pest management models only based on chemical controls. Liu and Teng [5] studied a pest management model with spraying pesticides at a fixed time of the pest reproductive cycles.…”

Section: Introductionmentioning

confidence: 99%

A pest control model with birth pulse and residual and delay effects of pesticides

Huang

Liu

2019

Adv Differ Equ

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Pesticides often cause residual and delayed effects on pests. Considering these effects, we use a pollution emission model to simulate the process of spraying pesticides. Many pests reproduce only at a fixed time in a year. So a pest control model with birth pulse and spraying pesticides is proposed. Using the limit system of the developed model, we analyze the dynamics of the system. The stability of the trivial equilibrium and the positive equilibrium of the model is analyzed, and the threshold conditions of pest eradication and permanence of the system are given. We obtain the optimal frequency of spraying pesticides by numerical simulations. The important parameters related to the pest eradication or permanence of the system are given by analyzing the sensitivity of the parameters. Finally, biological explanations are provided.

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“…In fact, many biological phenomena such as bursting rhythm models in biology and pharmacokinetics or frequency modulated systems exhibit impulsive effects, and periodic and state-dependent impulsive effects are two commonly occurring ones. In recent years, state-dependent impulsive control strategies have been used in the study on the interaction between wild and transgenic mosquito populations [7], predator-prey systems [8][9][10][11], management 2 Discrete Dynamics in Nature and Society of pests and fisheries [12][13][14], pulse vaccination for human infectious diseases [15], and bioprocess models [16][17][18][19][20]. In bioprocess, self-cycling is a new approach to deal with important environmental problems [16], and for that reason it has become a subject of consideration presented in this work.…”

Section: Introductionmentioning

confidence: 99%

Dynamics Analysis and Biomass Productivity Optimisation of a Microbial Cultivation Process through Substrate Regulation

Sun¹,

Liu²,

Kasperski³

et al. 2016

Discrete Dynamics in Nature and Society

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A microbial cultivation process model with variable biomass yield, control of substrate concentration, and biomass recycle is formulated, where the biochemical kinetics follows an extension of the Monod and Contois models. Control of substrate concentration allows for indirect monitoring of biomass and dissolved oxygen concentrations and consequently obtaining high yield and productivity of biomass. Dynamics analysis of the proposed model is carried out and the existence of order-1 periodic solution is deduced with a formulation of the period, which provides a theoretical possibility to convert the state-dependent control to a periodic one while keeping the dynamics unchanged. Moreover, the stability of the order-1 periodic solution is verified by a geometric method. The stability ensures a certain robustness of the adopted control; that is, even with an inaccurately detected substrate concentration or a deviation, the system will be always stable at the order-1 periodic solution under the control. The simulations are carried out to complement the theoretical results and optimisation of the biomass productivity is presented.

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Impulsive Ecological Control Of A Stage-Structured Pest Management System

Cited by 25 publications

References 0 publications

The Dynamics of a Predator‐Prey System with State‐Dependent Feedback Control

The Dynamics of a Predator‐Prey System with State‐Dependent Feedback Control

A pest control model with birth pulse and residual and delay effects of pesticides

Dynamics Analysis and Biomass Productivity Optimisation of a Microbial Cultivation Process through Substrate Regulation

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