Complex dynamics of a prey-predator interaction model with Holling type-II functional response incorporating the effect of fear on prey and non-linear predator harvesting

Majumdar, Prahlad; Debnath, Surajit; Mondal, Bapin; Sarkar, Susmita; Ghosh, Uttam

doi:10.1007/s12215-021-00701-y

Cited by 10 publications

(4 citation statements)

References 39 publications

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“…It is clear from (32) that the singular optimal solution (x * , 𝑦 * , E * ) , where 𝑦 * is the positive root of the equation…”

Section: Optimal Harvestingmentioning

confidence: 99%

“…Based on a review of the existing literature, it appears that most of the authors comprise their models with the combined effects of fear-harvesting [10,32], fear-refuge [8,9], harvesting-refuge [33,34], and studied their models. In a recent study, Alabacy [35] developed a three-species model with the combined effects of fear-refuge-harvesting.…”

Section: Introductionmentioning

confidence: 99%

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An autonomous and nonautonomous predator–prey model with fear, refuge, and nonlinear harvesting: Backward, Bogdanov–Takens, transcritical bifurcations, and optimal control

Mondal

Sarkar

Ghosh

2023

Math Methods in App Sciences

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In recent research, fear, refuge, and harvesting have been highlighted, but their combined impact must also be explored. We investigate the combined effects of these three ecologically important factors in the context of a prey–predator system using Holling type II as an interaction term. By using the parametric conditions, we can determine the existence of biologically feasible equilibria with their local and global stability. We investigate transcritical, Saddle‐node, Hopf, backward, Bogdanov–Takens bifurcations about different equilibria theoretically and numerically. We observe that the system is stable for lower and higher values of catchability effect and harvesting parameters. And the system shows stable behavior for a high value of fear and refuge parameters. Our model is extended by considering fear, refuge, and harvesting as time‐dependent parameters. Nonautonomous systems exhibit periodic solutions when the corresponding autonomous system is stable. Further, the nonautonomous system shows complex dynamics such as higher periods, chaos and bursting patterns whenever the associated autonomous system goes through limit cycle oscillations.

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“…It is clear from (32) that the singular optimal solution (x * , 𝑦 * , E * ) , where 𝑦 * is the positive root of the equation…”

Section: Optimal Harvestingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An autonomous and nonautonomous predator–prey model with fear, refuge, and nonlinear harvesting: Backward, Bogdanov–Takens, transcritical bifurcations, and optimal control

Mondal

Sarkar

Ghosh

2023

Math Methods in App Sciences

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“…There have been a variety of harvesting tactics used. Some of them used fixed harvesting, fixed effort harvesting (or proportional harvesting), and continuous threshold harvesting, while others examined nonlinear harvesting [22][23][24][25] .…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model

Jamil

Naji²

2023

Baghdad Sci.J

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A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify the validity of the theoretical analysis and visualize the model dynamics.

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“…Many other authors [10][11][12][13] investigated the impacts of toxicants, population, industrialization and pollution on forestry biomass. Literatures have also evidenced nonlinear mathematical models that explore harvesting of vegetation biomass and prey-predator [14][15][16][17][18][19]. In [20], authors found that predator harvesting can maintain the stability of the ecological system by terminating persistent oscillations.…”

Section: Introductionmentioning

confidence: 99%

Impacts of lockdown on the dynamics of forestry biomass, wildlife species and control of atmospheric pollution

Devi

Fatma

Verma

2022

Int. J. Dynam. Control

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In this paper, we have formulated and analysed a mathematical model to investigate the impacts of lockdown on the dynamics of forestry biomass, wildlife species and pollution. For this purpose, we have considered a nonlinear system of four ordinary differential equations representing rates of change of the density of forestry biomass, the density of wildlife species, the concentration of pollutants and lockdown. Conditions for the existence, uniqueness and local stability of all equilibria along with the global stability of the interior equilibrium point are derived. Furthermore, conditions that influence the persistence of the system are obtained. By formulating an optimal control problem, the optimal strategies for minimizing the cost of implementation of lockdown as well as the concentration of pollutants are also studied. Numerical simulations are carried out to verify and validate our analytical findings. By this study, we have observed that implementation of lockdown for a sufficient period of time minimizes excessive harvesting of both forestry biomass and wildlife species and the concentration of pollutants in the environment. It is also found that lockdown policy is effective in the optimal control of atmospheric pollution. Therefore, lockdown plays a significant role in the dynamics of forestry biomass, wildlife species and control of pollution in the environment.

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Complex dynamics of a prey-predator interaction model with Holling type-II functional response incorporating the effect of fear on prey and non-linear predator harvesting

Cited by 10 publications

References 39 publications

An autonomous and nonautonomous predator–prey model with fear, refuge, and nonlinear harvesting: Backward, Bogdanov–Takens, transcritical bifurcations, and optimal control

An autonomous and nonautonomous predator–prey model with fear, refuge, and nonlinear harvesting: Backward, Bogdanov–Takens, transcritical bifurcations, and optimal control

Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model

Impacts of lockdown on the dynamics of forestry biomass, wildlife species and control of atmospheric pollution

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