Conservation of a resource based fishery through optimal taxation

Pahari, U. K.; Kar, Tapan Kumar

doi:10.1007/s11071-012-0737-z

Cited by 16 publications

(10 citation statements)

References 14 publications

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“…We should point out that the simulation here should be considered as a qualitative, rather than a quantitative analysis. As described in Pahari and Kar, 13 using numerical simulation instead of real-world data has some advantages, numerous scenarios covering the breadth of the biological feasible parameter space were conducted, and the results display the gamut of dynamical results collected from all the scenarios tested. To study the relationship between the tax and the equilibrium, we maintain the values of the above parameters and change the value of in a certain range.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Kar investigated a ratio-dependent prey-predator model with selective harvesting of prey species only 10 and predator species only. 11 Lv et al 12 discussed the optimal taxation harvest policy for two-predator-one-prey system; meanwhile, Pahari and Kar 13 considered an optimal taxation harvest policy for the predator-prey model in which the predator is provided with an alternative food in addition to the prey species. Additionally, it should be mentioned that the harvesting policy related in above literature is specialist harvesting and can be influenced by a feedback mechanism.…”

Section: Introductionmentioning

confidence: 99%

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Optimal tax policy of a one‐predator–two‐prey system with a marine protected area

Huang

Cai

Liu

2021

Math Methods in App Sciences

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This paper is devoted to handle a dynamic one-predator-two-prey model. In order to protect fish population from over exploitation, we assume that marine protected area (MPA) is established and the fisherman only harvest the prey in the unreserved area, the predator consumes the prey in both the MPA and the unreserved area. And a tax is imposed in the process of harvesting. To begin with, boundeness of the system is discussed. Following this, we studied the existence of the possible equilibrium along with their local stability for both of the unexploited system (8) and exploited system (5). After that, we analyzed the global stability of the positive equilibrium of the exploited system and how the tax affects the positive equilibrium. Then, the optimal tax policy is obtained by using the Pontryagin's maximum principle. Finally, some numerical simulations are given to support the analytical findings.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal tax policy of a one‐predator–two‐prey system with a marine protected area

Huang

Cai

Liu

2021

Math Methods in App Sciences

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“…Again a prey-predator system plays an important role when an alternative source of food to the predator population is supplied (see Pahari and Kar [24], Srinivasu and Prasad [25], Srinivasu [26], Sabelis and van Rijn [27], Harwood and Obryeki [28], etc.). To control the pest, the effect of alternative food takes some attention compared to ordinary predatorprey dynamics in the context of biological conservation.…”

Section: Introductionmentioning

confidence: 99%

Prey-Predator Model with Two-Stage Infection in Prey: Concerning Pest Control

Nandi

Mondal²,

Jana³

et al. 2015

Journal of Nonlinear Dynamics

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A prey-predator model system is developed; specifically the disease is considered into the prey population. Here the prey population is taken as pest and the predators consume the selected pest. Moreover, we assume that the prey species is infected with a viral disease forming into susceptible and two-stage infected classes, and the early stage of infected prey is more vulnerable to predation by the predator. Also, it is assumed that the later stage of infected pests is not eaten by the predator. Different equilibria of the system are investigated and their stability analysis and Hopf bifurcation of the system around the interior equilibriums are discussed. A modified model has been constructed by considering some alternative source of food for the predator population and the dynamical behavior of the modified model has been investigated. We have demonstrated the analytical results by numerical analysis by taking some simulated set of parameter values.

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“…Xia et al [7] studied the combined effects of harvesting and time delay. Recently, Pahari and Kar [8] analyzed a prey-predator fishery model with harvesting where they applied a tax to regulate the fishery.…”

Section: Introductionmentioning

confidence: 99%

Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge

Das¹,

Kar

Pahari³

2013

ISRN Biomathematics

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This paper describes a prey-predator model with Holling type II functional response incorporating constant prey refuge and harvesting to both prey and predator species. We have analyzed the boundedness of the system and existence of all possible feasible equilibria and discussed local as well as global stabilities at interior equilibrium of the system. The occurrence of Hopf bifurcation of the system is examined, and it was observed that the bifurcation is either supercritical or subcritical. Influences of prey refuge and harvesting efforts are also discussed. Some numerical simulations are carried out for the validity of theoretical results.

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Conservation of a resource based fishery through optimal taxation

Cited by 16 publications

References 14 publications

Optimal tax policy of a one‐predator–two‐prey system with a marine protected area

Optimal tax policy of a one‐predator–two‐prey system with a marine protected area

Prey-Predator Model with Two-Stage Infection in Prey: Concerning Pest Control

Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge

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