Optimal harvesting strategy based on uncertain logistic population model

2021 ◽  
Vol 152 ◽  
pp. 111329
Author(s):  
Lifen Jia ◽  
Xueyong Liu
Keyword(s):  
Population Model ◽  
Optimal Harvesting

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>

STABILITY AND BIFURCATION ANALYSIS OF A DISCRETE PREY–PREDATOR MODEL WITH SQUARE-ROOT FUNCTIONAL RESPONSE AND OPTIMAL HARVESTING

2020 ◽  
Vol 28 (01) ◽  
pp. 91-110
Author(s):  
PRABIR CHAKRABORTY ◽  
UTTAM GHOSH ◽  
SUSMITA SARKAR
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Functional Response ◽  
Population Model ◽  
Optimal Harvesting ◽  
Herd Behavior ◽  
Square Root ◽  
Optimal Harvesting Policy ◽  
Optimal Value ◽  
Predator Model

In this paper, we have considered a discrete prey–predator model with square-root functional response and optimal harvesting policy. This type of functional response is used to study the dynamics of the prey–predator model where the prey population exhibits herd behavior, i.e., the interaction between prey and predator occurs along the boundary of the population. The considered population model has three fixed points; one is trivial, the second one is axial and the last one is an interior fixed point. The first two fixed points are always feasible but the last one depends on the parameter value. The interior fixed point experiences the flip and Neimark–Sacker bifurcations depending on the predator harvesting coefficient. Finally, an optimal harvesting policy has been introduced and the optimal value of the harvesting coefficient is determined.

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.

scholarly journals Optimal harvesting in an integrodifference population model

2006 ◽  
Vol 27 (2) ◽  
pp. 61-75 ◽  
Author(s):  
Hem Raj Joshi ◽  
Suzanne Lenhart ◽  
Holly Gaff
Keyword(s):  
Population Model ◽  
Optimal Harvesting
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