Slow–fast analysis of a modified Leslie–Gower model with Holling type I functional response

Saha, Tapan Kumar; Pal, Pallav Jyoti; Banerjee, Malay

doi:10.1007/s11071-022-07370-1

Cited by 17 publications

(5 citation statements)

References 45 publications

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“…Incorporating the empirical observation that the growth rate of predators is significantly lower than that of prey, the conventional predator-prey model becomes more ecologically realistic. In recent decades, there has been significant development in relevant mathematical theory pertaining to the exploration of properties of slow-fast dynamical systems [18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of a discrete Leslie–Gower predator–prey model with slow–fast effect on predator

Suleman,

Qadeer Khan,

Ahmed

2024

Math Methods in App Sciences

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Understanding and accounting for the slow–fast effect are crucial for accurately modeling and predicting the dynamics of predator–prey models, emphasizing the importance of considering the relative speeds of interacting populations in ecological research. This paper examines a predator–prey interaction to study its complex dynamics due to its slow–fast effect on predator populations. The occurrence and stability of equilibria are analyzed. The stability of positive fixed point is dependent on the slow–fast effect parameter , which must fall within a specific range when the generation gap is larger. The positive fixed point becomes unstable for bigger values of because the growth of predators is faster, resulting in the extinction of all prey. Smaller values of cause the positive fixed point to become unstable since the prey grows more quickly while the predator grows more slowly, ultimately causing the extinction of the predator. Moreover, it is shown that Leslie–Gower model experiences Neimark–Sacker and period‐doubling bifurcations at positive equilibrium point. In order to control bifurcation, hybrid control and feedback control methods are employed. Finally, analytical results are confirmed by numerical examples.

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Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of a discrete Leslie–Gower predator–prey model with slow–fast effect on predator

Suleman,

Qadeer Khan,

Ahmed

2024

Math Methods in App Sciences

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“…Also, they showed that the model under consideration experiences a number of bifurcations, which include saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation. Local and global stability analysis for the Leslie-Gower model and its modified model have been carried out by many researchers [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge

Vinoth¹,

Vadivel

et al. 2023

Mathematics

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Fear and prey refuges are two significant topics in the ecological community because they are closely associated with the connectivity of natural resources. The effect of fear on prey populations and prey refuges (proportional to both the prey and predator) is investigated in the nonlinear-type predator-harvested Leslie–Gower model. This type of prey refuge is much more sensible and realistic than the constant prey refuge model. Because there is less research on the dynamics of this type of prey refuge, the current study has been considered to strengthen the existing literature. The number and stability properties of all positive equilibria are examined. Since the calculations for the determinant and trace of the Jacobian matrix are quite complicated at these equilibria, the stability of certain positive equilibria is evaluated using a numerical simulation process. Sotomayor’s theorem is used to derive a precise mathematical confirmation of the appearance of saddle-node bifurcation and transcritical bifurcation. Furthermore, numerical simulations are provided to visually demonstrate the dynamics of the system and the stability of the limit cycle is discussed with the help of the first Lyapunov number. We perform some sensitivity investigations on our model solutions in relation to three key model parameters: the fear impact, prey refuges, and harvesting. Our findings could facilitate some biological understanding of the interactions between predators and prey.

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“…T. Saha, P.J. Pal, M. Banerjee [25] studied the slow-fast systems, including singular Hopf bifurcation, Bogdanov-Takens bifurcation, saddle-node bifurcation and boundary-equilibruium bifurcations. Some researchers have studied the dynamics of continuous slow-fast systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamics in a slow-fast Leslie-Gower predator-prey model with Beddington-DeAngelis functional response

Wang

2022

Preprint

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This paper deals with a class of Leslie-Gower predator-prey model with Beddington-DeAngelis functional response function. We assume that predator reproduce much slower than prey, which yield a slow-fast system. Using the normal form theory and geometric singular perturbation theory, we provide a detailed mathematical analysis for the existence of supercritical Hopf bifurcation, canard explosion and relaxation oscillation. Numerical simulations are also carried out to substantiate our analytical results.2000 Mathematics Subject Classification: 34C37, 34C07, 37G15.

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Slow–fast analysis of a modified Leslie–Gower model with Holling type I functional response

Cited by 17 publications

References 45 publications

Bifurcation analysis of a discrete Leslie–Gower predator–prey model with slow–fast effect on predator

Bifurcation analysis of a discrete Leslie–Gower predator–prey model with slow–fast effect on predator

Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge

Dynamics in a slow-fast Leslie-Gower predator-prey model with Beddington-DeAngelis functional response

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