Optimal harvesting of prey–predator system with interval biological parameters: A bioeconomic model

Pal, D.; Mahaptra, G.S.; Samanta, G. P.

doi:10.1016/j.mbs.2012.11.007

Cited by 141 publications

(60 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If we neglect the roles of the intra-specific competitive rates of the prey and predator, and the prey refuges, then system (1.5) can be reduced to equations (7) and (8) in [17]. In this paper, some results which are different from that in [17] are obtained.…”

Section: Preprintmentioning

confidence: 88%

“…Optimal harvesting problem have been studied in environmental and renewable resource economics. A lot of good work on this topic is emerged in recent years (see [13,14,15,16,17,18,19] in detail). Song and Chen [15] researched a competitive population model of two species with harvesting.…”

Section: Preprintmentioning

confidence: 99%

“…Song and Chen [15] researched a competitive population model of two species with harvesting. The study of one prey one predator harvesting model with imprecise biological parameters was presented by Pal et al in [17]. Liu and Bai [19] gained the optimal harvesting policy for a stochastic predator-prey model.…”

Section: Preprintmentioning

confidence: 99%

“…Stochastic approach, fuzzy approach, fuzzy-stochastic approach, etc. are useful approaches in managing the models with imprecise parameters, see [17,18,19] for example. In this contribution, we prepare to discuss imprecise parameters using fuzzy approach.…”

Section: Preprintmentioning

confidence: 99%

See 3 more Smart Citations

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

et al. 2015

View full text Add to dashboard Cite

This article concerns with the optimal harvesting of a predator-prey model with prey refuge and imprecise biological parameters. We consider the above model under impreciseness and introduce parametric functional form of an interval which are different from that of models with precise biological parameters. We study the existence and stability of the equilibria. The bionomic equilibria of the model are discussed. Also, the optimal harvesting policy is derived by using Pontryagin's maximal principle. Numerical simulations are presented to verify the feasibility of our analytical results.

show abstract

Section: Preprintmentioning

confidence: 88%

Section: Preprintmentioning

confidence: 99%

Section: Preprintmentioning

confidence: 99%

Section: Preprintmentioning

confidence: 99%

See 2 more Smart Citations

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

et al. 2015

View full text Add to dashboard Cite

show abstract

“…[20][21][22][23][24]proposed prey-predator harvesting model under impreciseness by considering biological parameters as interval number, Naji and Mustafa [19] studied the dynamics of an eco-epidemiological model with nonlinear incidence rate. Majeed and Shawka studied prey-predator model involving SI and SIS infectious disease in prey population and the disease transmitted within the same species by contact and external…”

Section: …………………………………………………………………………………………………… Introduction:-mentioning

confidence: 99%

A Food Chain Structures and Dynamics Across a Refuge Stage- Structure Prey-Predator Model.

Majeed¹,

Rahi.²

2017

IJAR

View full text Add to dashboard Cite

In the present paper the structures and dynamics of a food chain preypredator model are proposed and studied. The two stages and refuge in prey and two predators (top and mid) are considered. Different types of functional responses have been proposed. The conditions, which guarantee the existence of equilibrium points, have been investigated. Uniqueness and boundedness of the solution of the system are proven. The local and global dynamical behaviors are discussed and analyzed. Finally, numerical simulations are carried out not only to confirm the theoretical results obtained, but also to show the effects of the refuge and the variation of each parameter on our proposed system. …………………………………………………………………………………………………….... Introduction:-The first pattern formation of predator-prey model was introduced in 1927 by the well-known Lotka[15] and Volterra[28] which starting from a simple and classical supposition, more complexity but factual predator-prey models have been constructed by mathematicians and ecologists. In 1992, Berryman [6] considered that the dynamic interaction between predators and preys has long taken and go on to be one of the most important and central subjects which play a great role in each of the mathematical ecology, natural, social, and technological sciences, especially in the research on biology and ecology [5,17,26,27].Many researchers working in these fields paying a great amount of attention to improve and generalize the pattern formation of prey-predator models to more involvement and realistic system, and merging this advantage into many applications that give the nature of existence and global asymptotic stability of predator-prey models a great interest.On the other hand, the dynamical behavior of prey-predator models has been investigated by a lot of articles and peppers which results a significant expansion in the structural of the prey -predator models to involve multispecies; different functional responses, several types of food chain, refuge, harvesting, stage-structure, several types of diseases…etc.Lately, Samantha[25] studied the existence and global asymptotic stability of a delay predator-prey model with disease in the prey, Paletal. [20][21][22][23][24]proposed prey-predator harvesting model under impreciseness by considering biological parameters as interval number, Naji and Mustafa [19] studied the dynamics of an eco-epidemiological model with nonlinear incidence rate. Majeed and Shawka studied prey-predator model involving SI and SIS infectious disease in prey population and the disease transmitted within the same species by contact and external

show abstract

Near‐optimal control for a stochastic SIRS model with imprecise parameters

Zhang

Liang

2019

Asian Journal of Control

View full text Add to dashboard Cite

Parameter values are usually assumed to be precisely known in many epidemic models but they could be imprecise due to various uncertainties. In this paper, we develop a stochastic SIRS model that includes imprecise parameters and white noise, formulate and analyze the near‐optimal control problem for the stochastic model. We obtain priori estimates of the susceptible, infected and recovered populations. Sufficient and necessary conditions for the near optimality of the model are established using Ekeland's principle and a nearly maximum condition on the Hamiltonian function. Numerical simulations are also performed to demonstrate the analytical results and evaluate the influence of imprecise parameters, white noise and treatment control on the dynamics of epidemics.

show abstract

Optimal harvesting of prey–predator system with interval biological parameters: A bioeconomic model

Cited by 141 publications

References 23 publications

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

A Food Chain Structures and Dynamics Across a Refuge Stage- Structure Prey-Predator Model.

Near‐optimal control for a stochastic SIRS model with imprecise parameters

Contact Info

Product

Resources

About