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

Khan, Ihsan Ullah; Tang, Sanyi; Tang, Biao

doi:10.1155/2019/6509867

Cited by 8 publications

(2 citation statements)

References 38 publications

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“…e special case of model (2) for 휔 = 0 and − = is which has been considered in [47]. We will see that the results associated to model (8) can be easily obtained based on the results for model (2).…”

Section: Construction Of Model and Main Propertiesmentioning

confidence: 87%

The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control

Khan

Tang

2020

Discrete Dynamics in Nature and Society

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e idea of action threshold depends on the pest density and its change rate is more general and furthermore can produce new modelling techniques related to integrated pest management (IPM) as compared with those that appeared in earlier studies, which definitely bring challenges to analytical analysis and generate new ideas to the state control measures. Keeping this in mind, using the strategies of IPM, we develop a prey-predator system with action threshold depending on the pest density and its change rate, and study its dynamical behavior. We develop new criteria guaranteeing the existence, uniqueness, local and global stability of order-1 periodic solutions. Applying the properties of Lambert function, the Poincaré map is portrayed for the exact phase set, which is helpful to provide the sufficient conditions for the existence and stability of the interior order-1 periodic solutions and boundary order-1 periodic solution, also confirmed by numerical simulations. It is studied in detail that how and under what conditions the fixed point of Poincaré map and its stability are affected by the newly introduced action threshold. e analytical methods developed in this paper will be very beneficial to study other generalized models with state-dependent feedback control.Hindawi is a trajectory tangent to curve Γ at point 푆 = 푥 , 푦 , Γ 2 is a trajectory tangent to curve Γ at point 푇 = 푥 , 푦 , Γ 3 is homoclinic trajectory which touches curve Γ at two points 푥 1 , 푦 1 and 푥 2 , 푦 2 , and its upper and lower right branches touch curve Γ at points 푄 1 = 푥 푄 1 , 푦 푄 1 and 푄 2 = 푥 푄 2 , 푦 푄 2 , respectively.3 Discrete Dynamics in Nature and Society weighted parameters on the fixed point of Poincaré map. In the same section, the effect of weighted parameters on the different cases is also discussed. To sum up the whole work, a detailed conclusion is given in Section 7.

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Section: Construction Of Model and Main Propertiesmentioning

confidence: 87%

The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control

Khan

Tang

2020

Discrete Dynamics in Nature and Society

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“…In [38], Tian et al extended the classic pest-natural enemy model with linear state-dependent control measures to a model with nonlinear statedependent impulsive control tactics. In [39], the authors for the first time introduced and provided the concept of action threshold depending on the density of pest and its rate of change. ey used the definition and properties of the Lambert W function to construct the analytical expression of the Poincaré map.…”

Section: Model Construction and Main Properties Of Action Thresholdmentioning

confidence: 99%

A State‐Dependent Impulsive Nonlinear System with Ratio‐Dependent Action Threshold for Investigating the Pest‐Natural Enemy Model

Khan

Ullah

Bonyah³

et al. 2022

Complexity

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Based on the Lotka–Volterra system, a pest-natural enemy model with nonlinear feedback control as well as nonlinear action threshold is introduced. The model characterizes the implementation of comprehensive prevention and control measures when the pest density reaches the nonlinear action threshold level depending on the pest density and its change rate. The mortality rate of the pest is a saturation function that strictly depends on their density while the release of natural enemies is also a nonlinear pulse term depending on the density of real-time natural enemies. The exact impulsive and phase sets are given. The definition and properties of the Poincaré map corresponding to the pulse points on the phase set are provided. We investigate the existence and stability of boundary and interior order-1 periodic solution. The theoretical analysis developed in the present paper combined with nonlinear controlling measures as well as nonlinear action threshold methods and techniques laid the foundation for the establishment and analysis of other state-dependent feedback control models.

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A mosquito population suppression model with a saturated Wolbachia release strategy in seasonal succession

et al. 2023

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

Cited by 8 publications

References 38 publications

The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control

The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control

A State‐Dependent Impulsive Nonlinear System with Ratio‐Dependent Action Threshold for Investigating the Pest‐Natural Enemy Model

A mosquito population suppression model with a saturated Wolbachia release strategy in seasonal succession

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