Optimal Harvesting of a Spatially Explicit Fishery Model

Ding, Wandi; Lenhart, Suzanne

doi:10.1111/j.1939-7445.2008.00033.x

Cited by 28 publications

(33 citation statements)

References 33 publications

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“…By minimizing an intrinsic biological energy function which is different from the yield, they obtained an optimal spatial harvesting strategy which would benefit the population. Ding and Lenhart [14] considered an optimal fishery harvesting problem using a spatially explicit model with a semilinear elliptic PDE, Dirichlet boundary conditions and logistic population growth. They considered two objective functionals: maximizing the yield and minimizing the cost or the variation in the fishing effort (control).…”

Section: Introductionmentioning

confidence: 99%

Optimal control of growth coefficient on a steady-state population model

Ding

Finotti

Lenhart

et al. 2010

Nonlinear Analysis: Real World Applications

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Section: Introductionmentioning

confidence: 99%

Optimal control of growth coefficient on a steady-state population model

Ding

Finotti

Lenhart

et al. 2010

Nonlinear Analysis: Real World Applications

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“…In (Kelly et al. []) the models from (Neubert [], Ding and Lenhart []) are extended to Robin boundary conditions, and a finite time horizon, with a discounted profit of the form

J = \int_{0}^{T} \int_{Ω} p e^{- ρ t} h (x, t) u (x, t) d x d t

, where

p, ρ > 0

denote the price and discount rate, h is the harvest, and u the (fish) population density, which fulfills a rather general semilinear parabolic equation including advection. The first focus is again on well‐posedness and the first‐order optimality conditions, and numerical simulations are presented for some specific model choices, illustrating the dynamic formation and evolution of marine reserves.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Optimal Harvesting and Spatial Patterns in a Semiarid Vegetation System

Uecker

2016

Natural Resource Modeling

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We consider an infinite time horizon spatially distributed optimal harvesting problem for a vegetation and soil water reaction diffusion system, with rainfall as the main external parameter. By Pontryagin's maximum principle we derive the associated four component canonical system, and numerically analyze this and hence the optimal control problem in two steps. First we numerically compute a rather rich bifurcation structure of flat (spatially homogeneous) and patterned canonical steady states (FCSS and PCSS, respectively), in 1D and 2D. Then we compute time dependent solutions of the canonical system that connect to some FCSS or PCSS. The method is efficient in dealing with non-unique canonical steady states, and thus also with multiple local maxima of the objective function. It turns out that over wide parameter regimes the FCSS, i.e., spatially uniform harvesting, are not optimal. Instead, controlling the system to a PCSS yields a higher profit. Moreover, compared to (a simple model of) private optimization, the social control gives a higher yield, and vegetation survives for much lower rainfall. In addition, the computation of the optimal (social) control gives an optimal tax to incorporate into the private optimization.

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“…The optimal control problem for the combined harvesting of two competing species [10,11] including a predator have been discussed [13,37,49,57]. An optimal fishery harvesting problem using a spatially explicit model with a semi-linear elliptic PDE, Dirichlet boundary conditions, and logistic population growth was considered in [23], and results for maximizing the yield with the Neumann (noflux) boundary conditions are given. The proposed model differ from previous ones, especially that of Kar and Chaudhuri [39] in the sense that we do not consider interference or competition between the two preys.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of fisheries with prey reserve and harvesting

Khamis¹,

Tchuenche

Lukka

et al. 2011

International Journal of Computer Mathematics

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A model for two fish species and one predator in a patchy environment is formulated using a deterministic model to study the dynamics of fishery in two homogeneous patches, a free fishing zone and a refuge for prey reserve in which fishing is prohibited. The system is analysed around steady states; the criteria for local and global stabilities are established. The existence of bionomic equilibrium of the system is determined and the conditions for their existence are derived. The optimal harvesting policy is studied by using Pontryagin's maximal principle. Sensitivity analysis is carried out and it is observed that the populations are more sensitive to growth, dispersal and predation rates, least sensitive to the catchability coefficient. Statistical analysis is employed to estimate the parameters and to assess both the uncertainty in the model parameters and in the model-based predictions. Graphical representations of the model are provided.

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Optimal Harvesting of a Spatially Explicit Fishery Model

Cited by 28 publications

References 33 publications

Optimal control of growth coefficient on a steady-state population model

Optimal control of growth coefficient on a steady-state population model

Optimal Harvesting and Spatial Patterns in a Semiarid Vegetation System

Dynamics of fisheries with prey reserve and harvesting

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