The dynamics of a harvested predator–prey system with Holling type IV functional response

Liu, Xinxin; Huang, Qingdao

doi:10.1016/j.biosystems.2018.05.005

Cited by 33 publications

(19 citation statements)

References 21 publications

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“…In this sub-section, a mathematical model of predator-prey is analyzed by observing the distance between predators and prey which refers to a paper written by Liu and Huang (2018) [12]. The model used consists of two compartments, population of prey species and population of predator species .…”

Section: B the Mathematical Model Of Predator-prey By Observing The mentioning

confidence: 99%

“…In this paper, the mathematical model of predator-prey written by Liu and Huang (2018) will be reviewed by changing the functional response of Holling IV to a distance response between predators and prey, and eliminating harvesting factors [12]. With the condition of short distance between predators and prey, there is an increase in the prey process.…”

Section: Introductionmentioning

confidence: 99%

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Examination of Stability of the Mathematical Predator-Prey Model by Observing the Distance between Predator and Prey

Priyasih,

Miswanto,

Alfiniyah

2019

IJEAT

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Maintaining distance is one of the strategies that can be applied by prey to defend themselves or to avoid predatory attacks. This defense behavior can affect predation rates. The distance or difference in the number of prey and predator populations will affect the level of balanced ecosystem. The distance is also affecting predation rate, when there’s a long distance between prey and predator thus the predation rate decreases and vice versa. The purpose of this thesis is to analyze the stability of the mathematical equilibrium on predator-prey model by observing the distance. There are two types of model being observed, type one uses exponential growth model and type two is using a logistic growth model. The analytics results obtain three equilibrium points, namely the unstable extinction equilibrium point, and the asymptotically stable predator extinction with certain conditions and asymptotically stable coexistence with certain conditions. Then numerical simulation is conducted to support the analytical results.

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Section: B the Mathematical Model Of Predator-prey By Observing The mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Examination of Stability of the Mathematical Predator-Prey Model by Observing the Distance between Predator and Prey

Priyasih,

Miswanto,

Alfiniyah

2019

IJEAT

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“…In fact, the traditional Lotka-Volterra model serves as the basis for many models used today to analyze population dynamics. Many of the well-known proposed classical models were developed by many researchers taking into consideration various environmental factors that affect the existence and stability of this system, such as prey refuge [3][4][5], disease, [6,7], delay [8], harvesting [9] and many other factors [10][11][12][13]. Note that, the Lotka-Volterra prey-predator model in its general form can be expressed by [14]:…”

Section: Introductionmentioning

confidence: 99%

The Dynamics of Sokol-Howell Prey-Predator Model Involving Strong Allee Effect

Al-Momen

Naji

2021

Iraqi Journal of Science

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In this paper, a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

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“…They showed analytically and numerically that the discrete model is dynamically consistent with its continuous model. Liu and Huang [21] investigated the dynamical behavior of a predator-prey system with Holling type IV functional response, in which both species are subject to harvesting. They illustrated that using the harvesting effort as a control parameter can change the behaviors of the system, which may be useful for the biological management.…”

Section: Introductionmentioning

confidence: 99%

Chaos in a Hybrid Food Chain Model

Ali

Almohasin

Atewi

et al. 2021

eijs

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In this paper, chaotic and periodic dynamics in a hybrid food chain system with Holling type IV and Lotka-Volterra responses are discussed. The system is observed to be dissipative. The global stability of the equilibrium points is analyzed using Routh-Hurwitz criterion and Lyapunov direct method. Chaos phenomena is characterized by attractors and bifurcation diagram. The effect of the controlling parameter of the model is investigated theoretically and numerically.

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The dynamics of a harvested predator–prey system with Holling type IV functional response

Cited by 33 publications

References 21 publications

Examination of Stability of the Mathematical Predator-Prey Model by Observing the Distance between Predator and Prey

Examination of Stability of the Mathematical Predator-Prey Model by Observing the Distance between Predator and Prey

The Dynamics of Sokol-Howell Prey-Predator Model Involving Strong Allee Effect

Chaos in a Hybrid Food Chain Model

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