A non-autonomous Leslie–Gower model with Holling type IV functional response and harvesting complexity

Song, Jie; Xia, Yonghui; Bai, Yuzhen; Cai, Yaoxiong; O’Regan, Donal

doi:10.1186/s13662-019-2203-4

Cited by 16 publications

(6 citation statements)

References 37 publications

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“…Yu [18] menggunakan modifikasi model mangsa pemangsa Leslie-Gower yang dikemukakan dalam penelitian [1] dan menggunakan fungsi respon Beddington-DeAngelis. Beberapa modifikasi lainnya dapat dilihat dalam [2,4,5,9,13,14,16,19].…”

Section: Pendahuluanunclassified

Dynamics Analysis of Modified Leslie-Gower Model with Simplified Holling Type IV Functional Response

Ramadhani

Toaha

Kasbawati

2021

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In this paper, the modified Leslie-Gower predator-prey model with simplified Holling type IV functional response is discussed. It is assumed that the prey population is a dangerous population. The equilibrium point of the model and the stability of the coexistence equilibrium point are analyzed. The simulation results show that both prey and predator populations will not become extinct as time increases. When the prey population density increases, there is a decrease in the predatory population density because the dangerous prey population has a better ability to defend itself from predators when the number is large enough.

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Section: Pendahuluanunclassified

Dynamics Analysis of Modified Leslie-Gower Model with Simplified Holling Type IV Functional Response

Ramadhani

Toaha

Kasbawati

2021

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“…There are different types of functional response functions. Among them, Holling Type-I to Holling Type-IV [14][15][16][17][18] have frequently been used to model the predator and prey interactions. Although the Holling Type-II functional response has been most commonly used in the traditional predator-prey models.…”

Section: Establishment Of Modelmentioning

confidence: 99%

“…If r ≤ T holds, then there is no positive root for Equation (15). If r > T and Δ 1 > 0 hold, there are two positive roots for Equation (15). Define…”

Section: Existence and Local Stability Of Equilibrium Pointsmentioning

confidence: 99%

Dynamics of a pest management model with mate‐finding Allee effect induced by sterile release

Yue

Wang

2021

Math Methods in App Sciences

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Using sterile insect release to guide the occurrence of the mate-finding Allee effect in pest populations is considered a pest management strategy. In this paper, a pest management model is established with the mate-finding Allee effect induced by releasing sterile pests. In addition, the natural enemies of pests and spraying insecticide are also taken into account to achieve integrated pest management. For the model without delay, although the origin is not well-defined in our model, we pay attention to the dynamics near the origin and find it is always an attractor. This means the extinction of pests is closely related to their initial scale. Based on that, we conduct a detailed qualitative study on other equilibria. Furthermore, the model with a time delay is also observed. The stability of equilibrium points, Hopf bifurcation, and Bogdanov-Takens bifurcation are all carried out. Through numerical simulation, the results indicate that adding the mate-finding Allee effect can significantly reduce the demand for pesticides and reduce the environmental damage from pesticides, comparing with the traditional approach (i.e., combining natural enemies and pesticides).We also find that a time delay can switch the stability of the equilibrium points and promote the extinction of pests.

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“…One can easily find different modern works on various categories of the fractional differential equations and inclusions, [31][32][33][34][35][36] boundary value problems, [37][38][39][40][41][42] and modeling of different natural phenomena. [43][44][45][46][47][48][49][50][51] In 2016, Ahmad et al studied the existence results for the sequential fractional integro-differential equation with sum boundary value conditions:…”

Section: Introductionmentioning

confidence: 99%

“…They also use another approaches and methods for their special aims such as approximate methods and topological methods. One can easily find different modern works on various categories of the fractional differential equations and inclusions, 31‐36 boundary value problems, 37‐42 and modeling of different natural phenomena 43‐51 …”

Section: Introductionmentioning

confidence: 99%

On a fractional Caputo–Hadamard inclusion problem with sum boundary value conditions by using approximate endpoint property

Etemad

Rezapour

Samei

2020

Math Methods in App Sciences

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In the present research manuscript, we introduce a novel general fractional boundary value inclusion problem and investigate the necessary and sufficient conditions for desired existence results. Indeed, more precisely, we formulate a class of fractional multiterm Caputo-Hadamard differential inclusion problem with two-point sum boundary value conditions. In two separate theorems, we prove the existence results for mentioned inclusion problem by using-contractive maps and approximate endpoint property. Finally, we provide an example to illustrate our main results.

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A non-autonomous Leslie–Gower model with Holling type IV functional response and harvesting complexity

Cited by 16 publications

References 37 publications

Dynamics Analysis of Modified Leslie-Gower Model with Simplified Holling Type IV Functional Response

Dynamics Analysis of Modified Leslie-Gower Model with Simplified Holling Type IV Functional Response

Dynamics of a pest management model with mate‐finding Allee effect induced by sterile release

On a fractional Caputo–Hadamard inclusion problem with sum boundary value conditions by using approximate endpoint property

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