Conservation of an Ecosystem through Optimal Taxation

Krishna, S.

doi:10.1006/bulm.1997.0023

Cited by 52 publications

(18 citation statements)

References 6 publications

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“…Harvesting the biological resources can be introduced in the predator-prey model see, [3,4,12]. By incorporating nonlinear harvesting into the model (1) and assuming n 1 = n 2 , we get…”

Section: Accepted Manuscriptmentioning

confidence: 99%

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Stability and dynamics of a fractional order Leslie–Gower prey–predator model

Ghaziani

Alidousti

Eshkaftaki

2016

Applied Mathematical Modelling

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“…Harvesting the biological resources can be introduced in the predator-prey model see, [3,4,12]. By incorporating nonlinear harvesting into the model (1) and assuming n 1 = n 2 , we get…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…,(10),(11),(12) with the initial conditions (13) by using the well known Runge-Kutta method of order fourth and depict orbits of the system(5)for different set of parameters. For convenience, we fix the parameter values β = 2, l = 0.33, α = 0.8, k = 0.1, σ = 0.17, δ = 0.01, M = 5, h = 0.01 and vary the parameter γ.…”

mentioning

confidence: 99%

Stability and dynamics of a fractional order Leslie–Gower prey–predator model

Ghaziani

Alidousti

Eshkaftaki

2016

Applied Mathematical Modelling

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“…However, it is important to note that effect (i.e., reaper, equipment and other instruments) also act as the predator. If the handing time is taken into account to catch the prey species, then the above unrealistic features can largely be removed by adopting the alternative functional form [20] ( , )…”

Section: The Establishment Of Modelmentioning

confidence: 99%

Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation

Zhang¹,

Wang²,

Qin³

2015

ACM

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This paper deals with a discrete-time prey-predator system with Holling type-IV function response in the presence of some alternative food to predator and harvesting of prey species. By theoretical analysis and numerical simulation, comparing with the system without harvesting, ecological equilibrium point of the system is removed if harvesting effort is changed, and the appropriate harvesting effort can increase the stability of the system. Moreover, optimal harvesting policy is obtained using Pontryagin's maximum principle. Meanwhile, some numerical simulations verify our analytical results. This study also gains the maximum economic profit which is based on the ecological equilibrium. The suitable price of resources can control the excessive harvest to promote the sustainable development of species.

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“…For the details of this kind of harvesting one can see the Refs. [30,12,31]. The model (1) with nonlinear harvesting (Michaelis-Menten type) under the assumption that the extent to which the environment provides protection to both the predator and prey is the same [28,29] (i.e.…”

Section: Model With Prey Harvestingmentioning

confidence: 99%

Bifurcation analysis of modified Leslie–Gower predator–prey model with Michaelis–Menten type prey harvesting

Gupta

Chandra

2013

Journal of Mathematical Analysis and Applications

212

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a b s t r a c tIn the present paper we discuss bifurcation analysis of a modified Leslie-Gower prey-predator model in the presence of nonlinear harvesting in prey. We give a detailed mathematical analysis of the model to describe some significant results that may arise from the interaction of biological resources. The model displays a complex dynamics in the prey-predator plane. The permanence, stability and bifurcation (saddle-node bifurcation, transcritical, Hopf-Andronov and Bogdanov-Takens) of this model are discussed. We have analyzed the effect of prey harvesting and growth rate of predator on the proposed model by considering them as bifurcation parameters as they are important from the ecological point of view. The local existence and stability of the limit cycle emerging through Hopf bifurcation is given. The emergence of homoclinic loops has been shown through simulation when the limit cycle arising though Hopf bifurcation collides with a saddle point. This work reflects that the feasible upper bound of the rate of harvesting for the coexistence of the species can be guaranteed. Numerical simulations using MATLAB are carried out to demonstrate the results obtained.

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Conservation of an Ecosystem through Optimal Taxation

Abstract: In this paper we study a harvesting problem in the presence of a predator and a tax. The objective is to maximize the monetary social benefit as well as prevent the predator from extinction, keeping the ecological balance.

Cited by 52 publications

References 6 publications

Stability and dynamics of a fractional order Leslie–Gower prey–predator model

Stability and dynamics of a fractional order Leslie–Gower prey–predator model

Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation

Bifurcation analysis of modified Leslie–Gower predator–prey model with Michaelis–Menten type prey harvesting

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