Theory of optimal harvesting for a nonlinear size-structured population in periodic environments

2014 ◽  
Vol 07 (04) ◽  
pp. 1450046 ◽  
Author(s):  
Ze-Rong He ◽  
Rong Liu
Keyword(s):  
Renewable Resources ◽  
Population Model ◽  
Normal Cone ◽  
Optimal Harvesting ◽  
Well Posedness ◽  
Structured Population Model ◽  
First Order ◽  
Periodic Environment ◽  
Structured Population ◽  
Periodic Environments

This paper investigates the theoretical aspects for an optimal harvesting problem of a nonlinear size-structured population model in a periodic environment. We establish the well-posedness of the state system by means of frozen coefficients and fixed point reasoning. The existence of a unique optimal policy is proved via Ekeland's variational principle, and the first-order optimality conditions are derived by a suitable normal cone and a dual system. The results obtained would be beneficial for exploration of renewable resources.

ON THE WELL-POSEDNESS OF A NONLINEAR HIERARCHICAL SIZE-STRUCTURED POPULATION MODEL

2017 ◽  
Vol 58 (3-4) ◽  
pp. 482-490
Author(s):  
YAN LIU ◽  
ZE-RONG HE
Keyword(s):  
Comparison Principle ◽  
Existence And Uniqueness ◽  
Population Model ◽  
Time Dependent ◽  
Well Posedness ◽  
Vital Rates ◽  
Structured Population Model ◽  
Structured Population ◽  
Nonnegative Solutions

We analyse a nonlinear hierarchical size-structured population model with time-dependent individual vital rates. The existence and uniqueness of nonnegative solutions to the model are shown via a comparison principle. Our investigation extends some results in the literature.

scholarly journals Maximum principle for the optimal harvesting problem of a size-stage-structured population model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Miaomiao Chen ◽  
Rong Yuan
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Population Model ◽  
Dynamical Behavior ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Optimal Harvesting ◽  
Structured Population Model ◽  
Structured Population ◽  
Backward Euler

<p style='text-indent:20px;'>The optimal harvesting of biological resources, which is directly relevant to sustainable development, has attracted more attention. In this paper, we first prove the existence and uniqueness of generalized solution of a size-stage-structured population model while the optimal harvesting effort is discontinuous. Next, we demonstrate the existence of the optimal harvesting policy. Further, based on the idea of the Pontryagin's maximum principle of the optimal control problem in ordinary differential equations, we derive the maximum principle describing the optimal control. Finally, the dynamical behavior of the population is simulated by solving the corresponding optimality system numerically with an algorithm based on the method of backward Euler implicit finite-difference approximation. The numerical simulations indicate harvesting activity will reduce the quantity of the population and that increasing harvesting cost will result in less adult harvested. This provides guideline of implementing harvesting tactic to guarantee the persistence of the population.</p>

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