Diffusive logistic equation with constant yield harvesting, I: Steady States

Oruganti, Shobha; Shi, Junping; Shivaji, R.

doi:10.1090/s0002-9947-02-03005-2

Cited by 103 publications

(45 citation statements)

References 20 publications

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“…There are a few papers which study on population models with harvesting rates governed by reaction-diffusion equations [22,24,25]. One of these harvesting rates is the quasi-constant-yield harvest rate introduced by Roques and Chekroun [25] in 2007.…”

Section: Kunquan Lan and Wei Linmentioning

confidence: 99%

Population models with quasi-constant-yield harvest rates

Lan

Lin

2016

MBE

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One-dimensional logistic population models with quasi-constant-yield harvest rates are studied under the assumptions that a population inhabits a patch of dimensionless width and no members of the population can survive outside of the patch. The essential problem is to determine the size of the patch and the ranges of the harvesting rate functions under which the population survives or becomes extinct. This is the first paper which discusses such models with the Dirichlet boundary conditions and can tell the exact quantity of harvest rates of the species without having the population die out. The methodology is to establish new results on the existence of positive solutions of semi-positone Hammerstein integral equations using the fixed point index theory for compact maps defined on cones, and apply the new results to tackle the essential problem. It is expected that the established analytical results have broad applications in management of sustainable ecological systems.

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Section: Kunquan Lan and Wei Linmentioning

confidence: 99%

Population models with quasi-constant-yield harvest rates

Lan

Lin

2016

MBE

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“…11]. For modelling the fish population in a lake, we consider the same set of assumptions as taken by Oruganti, Shi, and Shivaji [OSS02], i. e.:…”

Section: Introductionmentioning

confidence: 99%

Optimal harvesting strategy based on rearrangements of functions

Emamizadeh

Farjudian

Liu

2018

Applied Mathematics and Computation

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We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum harvesting capacity. For this generalization, we need a completely different approach. As such, we use the theory of rearrangements of functions. We prove existence of solutions, and obtain an optimality condition which indicates that the more aggressive harvesting must be pushed towards the boundary of the domain. Furthermore, we prove that radial and Steiner symmetries of the domain are preserved by the solutions. We will also devise an algorithm for numerical solution of the problem, and present the results of some numerical experiments.

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“…When p = 1, (1.1) arises in population dynamics where 1/λ is the diffusion coefficient and ch(x) represents the constant yield harvesting. In this case (p = 1), when g(x) is a positive constant, various results have been established in [4]. Here we focus on sign changing weight functions g.…”

Section: Introductionmentioning

confidence: 99%

“…Note that when c > 0, (1.1) is a semipositone problem and it is well known in the literature that the study of positive solutions is mathematically challenging (see [2][3][4]). Here we also include the additional challenge of dealing with a sign changing weight function g.…”

Section: Introductionmentioning

confidence: 99%