Numerical Investigation of Fuzzy Predator-Prey Model with a Functional Response of the Form Arctan(ax)

Mallak, Saed F.; Farekh, Doa’a; Attili, Basem S.

doi:10.3390/math9161919

Cited by 4 publications

(4 citation statements)

References 25 publications

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“…Moreover, the authors in Narayanamoorthy et al [23], used the fractional modified Euler method. On the biological perspective, there are some authors who have studied fuzzy predator-prey models with functional responses such as [20,23,24,26]. They all studied a predator-prey model with fuzzy initial conditions.…”

Section: Introductionmentioning

confidence: 99%

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A Runge-Kutta numerical scheme applied in solving predator-prey fuzzy model with Holling type II functional response

Sukarsih

Supriatna

Carnia

et al. 2023

Front. Appl. Math. Stat.

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The predator-prey model has been extensively studied, but only studies models in a certain environment, where all parameters and initial values involved in the model are assumed to be certain. In real practice, some parameters and initial values are often uncertain. To overcome this uncertainty problem, a model can be made by using a fuzzy theoretical approach. In this paper, we develop a numerical scheme for solving two predator-prey models with a Holling type II functional response by considering fuzzy parameters and initial populations. The behavior of the model was studied qualitatively using the 5th order Runge-Kutta method of which was modified for the fuzzy system using the Zadeh extension principle. The numerical simulation results show that, when the initial populations of prey and predators are fuzzy, the behavior of the fuzzy model would be qualitatively the same as the crisp model. Finally, we conclude that the resulting fuzzy behavior represents a generalization of crisp behavior. This gives more realistic results since the solution is obtained by explicitly considering the problem of uncertainty.

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Section: Introductionmentioning

confidence: 99%

“…Their work studied two species of predator-prey harvesting models by considering fuzzy parameters. Among those work, the authors in Mallak et al [26], studied a fuzzy predator-prey model with an arctan functional response using the Hukuhara derivative approach, to describe the satiation predator's consumption.…”

Section: Introductionmentioning

confidence: 99%

A Runge-Kutta numerical scheme applied in solving predator-prey fuzzy model with Holling type II functional response

Sukarsih

Supriatna

Carnia

et al. 2023

Front. Appl. Math. Stat.

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show abstract

“…In view of the uncertainty in nature environment and imprecision in experimental measurement, it is a natural idea to use fuzzy parameters instead of fixed ones to make the model more reasonable. Many researchers concentrated their models under stochastic factors [19,20] and fuzzy conditions [21][22][23][24][25][26][27][28][29]. Pal et al [21] first introduced the fuzzy prey-predator model with fuzzy parameters instead of determined parameters, by introducing fuzzy interval number.…”

Section: Introductionmentioning

confidence: 99%

“…Yu et al [27] proposed a fuzzy prey-predator harvesting model that incorporates both the effects of prey refuge and predator mutual interference. Mallak and Farekh [28] investigated a fuzzy prey-predator model with a arctan(ax) type of functional response numerically. In above articles and relevant researches, almost all models involve a single imprecision index for different species.…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics of two prey–predator harvesting models with prey refuge and interval‐valued imprecise parameters

Tian

Hua

Sun

2023

Math Methods in App Sciences

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In view of the phenomena that species in nature are affected by the complexity of the ecosystem, some key biological parameters have certain inaccuracy or uncertainty and part of the prey hides in the shelter from predation. Moreover, different species exhibit different living habits, so it is of certain interest to investigate species‐related imprecise biological parameters. Besides, from the perspective of scientific and reasonable exploitation and utilization of fishery resources, two types of harvesting strategies are introduced into the system. Firstly, the dynamic properties of the system guided by continuous harvesting strategy are analyzed, which demonstrates the impact of refuge rate, imprecision indexes and harvesting efforts on the system dynamics. Meanwhile, the bio‐economic equilibrium is discussed, and the optimal harvesting strategy is obtained. Secondly, the complex dynamics of the system induced by weighted harvesting activity are analyzed. The predator‐extinction periodic solution and coexistent order‐1 periodic solution is discussed according to different weights and thresholds. Finally, the correctness of the obtained results and the feasibility of the harvesting strategy are verified through numerical simulation in MATLAB. The results of this study provide a reference for the scientific and reasonable exploitation and utilization of prey–predator fishery resources in the imprecise parameter environment.

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Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters

Tian¹,

Li²,

Liu³

2023

Chaos, Solitons & Fractals

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Numerical Investigation of Fuzzy Predator-Prey Model with a Functional Response of the Form Arctan(ax)

Cited by 4 publications

References 25 publications

A Runge-Kutta numerical scheme applied in solving predator-prey fuzzy model with Holling type II functional response

A Runge-Kutta numerical scheme applied in solving predator-prey fuzzy model with Holling type II functional response

Complex dynamics of two prey–predator harvesting models with prey refuge and interval‐valued imprecise parameters

Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters

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