On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population

Uddin, Md. Jasim; Rana, Sarker Md. Sohel; Işık, Seval; Kangalgil, Figen

doi:10.1016/j.chaos.2023.113932

Cited by 14 publications

(6 citation statements)

References 29 publications

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“…Their work motivates us to consider the discrete counterpart of system (1.3). In recent years, many researchers have studied the dynamical behavior of discrete fractional-order predator-prey systems and have discovered numerous intriguing dynamical properties within these systems [34][35][36].…”

Section: Parameter Meaningmentioning

confidence: 99%

Modeling and Dynamical Analysis of a Fractional-Order Predator–Prey System with Anti-Predator Behavior and a Holling Type IV Functional Response

Wang,

2023

Fractal Fract

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We here investigate the dynamic behavior of continuous and discrete versions of a fractional-order predator–prey system with anti-predator behavior and a Holling type IV functional response. First, we establish the non-negativity, existence, uniqueness and boundedness of solutions to the system from a mathematical analysis perspective. Then, we analyze the stability of its equilibrium points and the possibility of bifurcations using stability analysis methods and bifurcation theory, demonstrating that, under specific parameter conditions, the continuous system exhibits a Hopf bifurcation, while the discrete version exhibits a Neimark–Sacker bifurcation and a period-doubling bifurcation. After providing numerical simulations to illustrate the theoretically derived conclusions and by summarizing the various analytical results obtained, we finally present four interesting conclusions that can contribute to better management and preservation of ecological systems.

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Section: Parameter Meaningmentioning

confidence: 99%

Modeling and Dynamical Analysis of a Fractional-Order Predator–Prey System with Anti-Predator Behavior and a Holling Type IV Functional Response

Wang,

2023

Fractal Fract

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“…They showed that this model undergoes a Neimark-Sacker and a Period-doubling bifurcations under some certain conditions. The chaos in the dynamical system was also obtained in [3]. Lee and Baek [4] analysed a predator-prey system with Beddington-DeAngelis functional response with harvesting.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Uddin et al [3] investigated a discrete prey-predator system with harvesting on the predator species by using the Caputo fractional derivative. They showed that this model undergoes a Neimark-Sacker and a Period-doubling bifurcations under some certain conditions.…”

Section: Introductionmentioning

confidence: 99%

Qualitative Behavior for a Discretized Conformable Fractional-Order Lotka-Volterra Model With Harvesting Effects

Berkal,

Navarro,

Almatrafi

2024

Int. J. Anal. Appl.

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The predator-prey model is a widely mathematical structure that explains the dynamics between two interacting populations: predators and prey. The predator-prey interaction represents a fundamental dynamic in nature, influencing the stability and balance of ecosystems worldwide. The purpose of this article is to provide insight into the complex interactions and feedback mechanisms between predators and prey in ecological systems via mathematical tools such as stability and bifurcation. We investigate a fractional-order Lotka-Volterra model with a harvesting effect using stability and bifurcation theory. The equilibrium points and local stability of the purposed model are presented in this article. The bifurcation analysis, which is a potent approach used to analyse the qualitative behavior of the predator-prey system as the parameter values are varied, is also explored. In particular, a Neimark-Sacker bifurcation and a period-doubling bifurcation are theoretically and numerically examined. Furthermore, we illustrate some 2D figures to show the phase portriat and bifurcations of this model at various points.

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“…Ou et al [18] carried out a mathematical analysis of the bifurcation phenomenon and controller design of a class of delayed BAM neural networks. For more detailed publications, one can consult [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Exploration and Controller Design in a Fractional Oxygen–Plankton Model with Delay

Zhang,

2024

Fractal Fract

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Fractional-order differential equations have been proved to have great practical application value in characterizing the dynamical peculiarity in biology. In this article, relying on earlier work, we formulate a new fractional oxygen–plankton model with delay. First of all, the features of the solutions of the fractional delayed oxygen–plankton model are explored. The judgment rules on non-negativeness, existence and uniqueness and the boundedness of the solution are established. Subsequently, the generation of bifurcation and stability of the model are dealt with. Delay-independent parameter criteria on bifurcation and stability are presented. Thirdly, a hybrid controller and an extended hybrid controller are designed to control the time of onset of bifurcation and stability domain of this model. The critical delay value is provided to display the bifurcation point. Last, software experiments are offered to support the acquired key outcomes. The established outcomes of this article are perfectly innovative and provide tremendous theoretical significance in balancing the oxygen density and the phytoplankton density in biology.

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On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population

Cited by 14 publications

References 29 publications

Modeling and Dynamical Analysis of a Fractional-Order Predator–Prey System with Anti-Predator Behavior and a Holling Type IV Functional Response

Modeling and Dynamical Analysis of a Fractional-Order Predator–Prey System with Anti-Predator Behavior and a Holling Type IV Functional Response

Qualitative Behavior for a Discretized Conformable Fractional-Order Lotka-Volterra Model With Harvesting Effects

Bifurcation Exploration and Controller Design in a Fractional Oxygen–Plankton Model with Delay

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