scholarly journals On optimal harvesting of renewable resource from the structured population

2019 ◽  
Vol 29 (4) ◽  
pp. 501-517
Author(s):  
A.V. Egorova ◽  
◽  
L.I. Rodina ◽  
◽  
Keyword(s):  
Renewable Resource ◽  
Optimal Harvesting ◽  
Structured Population

Optimization of discounted income for a structured population exposed to harvesting

2021 ◽  
pp. 15-25
Author(s):  
Anastasia V. Egorova
Keyword(s):  
Time Moment ◽  
Renewable Resource ◽  
Optimal Harvesting ◽  
Infinite Time ◽  
System Of Difference Equations ◽  
Time Intervals ◽  
Homogeneous Population ◽  
Structured Population ◽  
The Cost ◽  
Conventional Unit

A structured population the individuals of which are divided into n age or typical groups x_1,…,x_n. is considered. We assume that at any time moment k, k = 0,1,2… the size of the population x(k) is determined by the normal autonomous system of difference equations x(k+1)=F(x(k)), where F(x)=col(f_1 (x),…,〖 f〗_n (x) ) are given vector functions with real non-negative components f_i (x), i=1,…n. We investigate the case when it is possible to influence the population size by means of harvesting. The model of the exploited population under discussion has the form x(k+1)=F((1-u(k) )x(k) ), where u(k)= (u_1 (k),…,u_n (k))∈〖[0; 1]〗^n is a control vector, which can be varied to achieve the best result of harvesting the resource. We assume that the cost of a conventional unit of each of n classes is constant and equals to C_i≥0, i=1,…,n. To determine the cost of the resource obtained as the result of harvesting, the discounted income function is introduced into consideration. It has the form H_α (u ̅,x(0))=∑_(j=0)^∞▒〖∑_(i=1)^n▒〖C_i x_i (j) u_i (j) e^(-αj) 〗,〗 where α>0 is the discount coefficient. The problem of constructing controls on finite and infinite time intervals at which the discounted income from the extraction of a renewable resource reaches the maximal value is solved. As a corollary, the results on the construction of the optimal harvesting mode for a homogeneous population are obtained (that is, for n = 1).

scholarly journals Optimal Harvesting Effort for Nonlinear Predictive Control Model for a Single Species Fishery

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Messaoud Bounkhel ◽  
Lotfi Tadj
Keyword(s):  
Predictive Control ◽  
Renewable Resource ◽  
Single Species ◽  
State Equation ◽  
Control Model ◽  
Optimal Harvesting ◽  
Solution Approach ◽  
Nonlinear Predictive Control ◽  
Nonlinear State ◽  
Resource System

We use nonlinear model predictive control to find the optimal harvesting effort of a renewable resource system with a nonlinear state equation that maximizes a nonlinear profit function. A solution approach is proposed and discussed and satisfactory numerical illustrations are provided.

scholarly journals A Mathematical Model for Optimal Management and Utilization of a Renewable Resource by Population

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
B. Dubey ◽  
Atasi Patra
Keyword(s):  
Output Feedback ◽  
Output Feedback Control ◽  
Hamiltonian Function ◽  
Renewable Resource ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Optimal Management ◽  
Crowding Effect ◽  
Stability Behavior ◽  
Theoretical Results

A dynamical model is proposed and analyzed to study the effect of the population on the resource biomass by taking into account the crowding effect. Biological and bionomical equilibria of the system are discussed. The global stability behavior of the positive equilibrium is studied via the output feedback control. An appropriate Hamiltonian function is formed for the discussion of optimal harvesting of resource which is utilized by the population using Pontryagin's Maximum Principal. A numerical simulation is performed on the model to analyze the theoretical results.

scholarly journals Optimal Harvesting for an Age-Spatial-Structured Population Dynamic Model with External Mortality

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yong Han Kang ◽  
Mi Jin Lee ◽  
Il Hyo Jung
Keyword(s):  
Dynamic Model ◽  
Population Dynamic ◽  
Total Population ◽  
Total Mortality ◽  
Optimal Harvesting ◽  
Uniqueness Of Solutions ◽  
Population Dynamic Model ◽  
Structured Population ◽  
Necessary Conditions For Optimality ◽  
Environmental Causes

We study an optimal harvesting for a nonlinear age-spatial-structured population dynamic model, where the dynamic system contains an external mortality rate depending on the total population size. The total mortality consists of two types: the natural, and external mortality and the external mortality reflects the effects of external environmental causes. We prove the existence and uniqueness of solutions for the population dynamic model. We also derive a sufficient condition for optimal harvesting and some necessary conditions for optimality in an optimal control problem relating to the population dynamic model. The results may be applied to an optimal harvesting for some realistic biological models.

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>

Optimal harvesting of a hierarchical age-structured population system

2019 ◽  
Vol 12 (08) ◽  
pp. 1950091 ◽  
Author(s):  
Ze-Rong He ◽  
Dongdong Ni ◽  
Shu-Ping Wang
Keyword(s):  
Optimal Strategies ◽  
Adjoint System ◽  
Optimal Harvesting ◽  
Normal Cones ◽  
Population System ◽  
The Maximum Principle ◽  
Structured Population ◽  
Continuity Result ◽  
Highly Nonlinear ◽  
Age Structured

We investigate an optimal harvesting problem for age-structured species, in which elder individuals are more competitive than younger ones, and the population is modeled by a highly nonlinear integro-partial differential equation with a global feedback boundary condition. The existence of optimal strategies is established by means of compactness and maximizing sequences, and the maximum principle obtained via an adjoint system, tangent-normal cones and a new continuity result. In addition, some numerical experiments are presented to show the effects of the price function and younger’s weight on the optimal profits.

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