A pest management model with state feedback control

Liu, Qiong; Huang, Lizhuang; Chen, Lansun

doi:10.1186/s13662-016-0985-1

Cited by 11 publications

(7 citation statements)

References 2 publications

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“…Note that if ≤ 0, then for any + ≥ 0, (17) and (18) are well defined. Actually, if we denote ( ) = −( / ) exp(−( / ) ), then it can easily be shown that…”

Section: Poincaré Map Let a Trajectory Initiate With Initial Valuementioning

confidence: 99%

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The State‐Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate

Khan

Tang

2019

Complexity

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Whether the integrated control measures are applied or not depends not only on the current density of pest population, but also on its current growth rate, and this undoubtedly brings challenges and new ideas to the state control measures that only rely on the pest density. To address this, utilizing the tactics of IPM, we constructed a Lotka-Volterra predator-prey system with action threshold depending on the pest density and its changing rate and examined its dynamical behavior. We present new criteria guaranteeing the existence, uniqueness, and global stability of periodic solutions. With the help of Lambert W function, the Poincaré map is constructed for the phase set, which can help us to provide the satisfactory conditions for the existence and stability of the semitrivial periodic solution and interior order-1 periodic solutions. Furthermore, the existence of order-2 and nonexistence of order-k(k≥3) periodic solutions are discussed. The idea of action threshold depending on the pest density and its changing rate is more general and can generate new remarkable directions as well compared with those represented in earlier studies. The analytical techniques developed in this paper can play a significant role in analyzing the impulsive models with complex phase set or impulsive set.

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“…Note that if ≤ 0, then for any + ≥ 0, (17) and (18) are well defined. Actually, if we denote ( ) = −( / ) exp(−( / ) ), then it can easily be shown that…”

Section: Poincaré Map Let a Trajectory Initiate With Initial Valuementioning

confidence: 99%

“…There are two main kinds of the classical impulsive differential equations: fixed-time impulse and state-dependent impulse. We refer readers to [12][13][14][15][16][17][18][19][20][21][22][23][24] for more details about the aforementioned kinds of classical impulsive differential equations and their application in different fields.…”

Section: Introductionmentioning

confidence: 99%

The State‐Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate

Khan

Tang

2019

Complexity

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“…For a long term in this way, the predator will be endangered, the ecological balance will also be destroyed. To avoid such a disaster, intervention has to be made, such as pest management and harvesting of fish [6][7][8][9][10][11][12][13][14][15]. Such interventions can be mathematically modeled by impulsive systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of a prey–predator model with state-dependent control strategy and square root response function

Liu

Cheng

2018

Adv Differ Equ

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In this work, a prey-predator model with square root response function under a state-dependent impulse is proposed. Firstly, according to the differential equation geometry theory and the method of successor function, the existence, uniqueness and attractiveness of the order-1 periodic solution are analyzed. Then the stability of the order-1 periodic solution is discussed by the Poincaré criterion for impulsive differential equations. Finally, we show a specific example and carry out numerical simulations to verify the theoretical results.

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“…In recent years, the theoretical studies on IDES have produced a lot of good research results [23][24][25][26][27][28][29][30][31][32][33][34]. Based on the theoretical research, some scholars have introduced impulsive differential equations in Lotka-Volterra system such as the regular release of predators [35][36][37]; the periodic release of infected pests [38][39][40]; the periodic release of predators together with regular spray of pesticides [41][42][43]; the periodic release of predators and infected pests together with regular spray of pesticides [39,44]. In the practical application, the two control measures can be adopted at two different levels of pest density concerning this case.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control

Liu

et al. 2018

Discrete Dynamics in Nature and Society

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The application of pest management involves two thresholds when the chemical control and biological control are adopted, respectively. Our purpose is to provide an appropriate balance between the chemical control and biological control. Therefore, a Smith predator-prey system for integrated pest management is established in this paper. In this model, the intensity of implementation of biological control and chemical control depends linearly on the selected control level (threshold). Firstly, the existence and uniqueness of the order-one periodic solution (i.e., OOPS) are proved by means of the subsequent function method to confirm the feasibility of the biological and chemical control strategy of pest management. Secondly, the stability of system is proved by the limit method of the successor points' sequences and the analogue of the Poincaré criterion. Moreover, an optimization strategy is formulated to reduce the total cost and obtain the best level of pest control. Finally, the numerical simulation of a specific model is performed. ̸ = ℎ 1 , ℎ 2 , = ℎ 1 , V > V * , Δ ( ) = 0,

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A pest management model with state feedback control

Cited by 11 publications

References 2 publications

The State‐Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate

The State‐Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate

Dynamic analysis of a prey–predator model with state-dependent control strategy and square root response function

Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control

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