Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

Panigoro, Hasan S.; Rahmi, Emli; Resmawan, Resmawan

doi:10.3389/fams.2022.1077831

Cited by 3 publications

(2 citation statements)

References 36 publications

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“…Predator-prey interaction, as the basis of the food chain, is among the most essential ecological issues. In numerous published research, mathematical models have been developed to explain the dynamics of Predator-prey interaction, such as by incorporating social behavior [1,2], age structure [3,4], ratio-dependent functional response [5,6], harvesting [7,8], and so on. The Predator-prey model is still being developed by considering many factors that occur in nature.…”

Section: Introductionmentioning

confidence: 99%

Dynamics analysis of a predator–prey fractional-order model incorporating predator cannibalism and refuge

Rayungsari

Suryanto

Kusumawinahyu

et al. 2023

Front. Appl. Math. Stat.

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In this article, we consider a predator–prey interaction incorporating cannibalism, refuge, and memory effect. To involve the memory effect, we apply Caputo fractional-order derivative operator. We verify the non-negativity, existence, uniqueness, and boundedness of the model solution. We then analyze the local and global stability of the equilibrium points. We also investigate the existence of Hopf bifurcation. The model has four equilibrium points, i.e., the origin point, prey extinction point, predator extinction point, and coexistence point. The origin point is always unstable, while the other equilibrium points are conditionally locally asymptotically stable. The stability of the coexistence point depends on the order of the Caputo derivative, α. The prey extinction point, predator extinction point, and coexistence point are conditionally globally and asymptotically stable. There exists Hopf bifurcation of coexistence point with parameter α. The analytic results of stability properties and Hopf bifurcations are confirmed by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Dynamics analysis of a predator–prey fractional-order model incorporating predator cannibalism and refuge

Rayungsari

Suryanto

Kusumawinahyu

et al. 2023

Front. Appl. Math. Stat.

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“…The journey of mathematical modeling has an important role in the wide area of ecological problems. Several researchers are interested in studying the interaction between two or more populations due to its contribution to describing the existence of populations in their ecosystem [1][2][3][4]. The famous ones are given by Lotka (1925) and Volterra (1926), which is defined by [5,6]…”

Section: Introductionmentioning

confidence: 99%

The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting

et al. 2023

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Modeling the interaction between prey and predator plays an important role in maintaining the balance of the ecological system. In this paper, a discrete-time mathematical model is constructed via a forward Euler scheme, and then studied the dynamics of the model analytically and numerically. The analytical results show that the model has two fixed points, namely the origin and the interior points. The possible dynamical behaviors are shown analytically and demonstrated numerically using some phase portraits. We show numerically that the model has limit-cycles on its interior. This guarantees that there exists a condition where both prey and predator maintain their existence periodically.

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Population dynamics in a Leslie–Gower predator–prey model with predator harvesting at high densities

Cortés García

2024

Math Methods in App Sciences

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In this paper, we propose a Leslie–Gower predator–prey model in which the predator can only be captured when its population size exceeds a critical value; the mean growth rate of the prey in the absence of the predator is subject to a semi‐saturation rate that affects its birth curve, and the interaction between the two species is defined by a Holling II predation functional with alternative food for the predator. Since the proposed model is equivalent to a Filippov system, its mathematical analysis leads to a local study of the equilibria in each vector field corresponding to the proposed model, in addition to the study of the stability of its pseudo‐equilibria located on the curve separating the two vector fields. In particular, the model could have between one and three pseudo‐equilibria and at least one limit cycle surrounding one or two inner equilibria, locally unstable points.

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Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

Cited by 3 publications

References 36 publications

Dynamics analysis of a predator–prey fractional-order model incorporating predator cannibalism and refuge

Dynamics analysis of a predator–prey fractional-order model incorporating predator cannibalism and refuge

The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting

Population dynamics in a Leslie–Gower predator–prey model with predator harvesting at high densities

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