scholarly journals Optimal Harvesting of a Spatial Renewable Resource

2012 ◽  
Author(s):  
Stefan Behringer ◽  
Thorsten Upmann
Keyword(s):  
Renewable Resource ◽  
Optimal Harvesting

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.

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 of a spatial renewable resource

2014 ◽  
Vol 42 ◽  
pp. 105-120 ◽  
Author(s):  
Stefan Behringer ◽  
Thorsten Upmann
Keyword(s):  
Renewable Resource ◽  
Optimal Harvesting

scholarly journals Optimal management of a renewable resource utilized by a population with taxation as a control variable

2013 ◽  
Vol 18 (1) ◽  
pp. 37-52 ◽  
Author(s):  
Balram Dubey ◽  
Atasi Patra
Keyword(s):  
Maximum Principle ◽  
Control Variable ◽  
Renewable Resource ◽  
Dynamical Variable ◽  
Dynamical Model ◽  
Optimal Harvesting ◽  
Optimal Management ◽  
Crowding Effect ◽  
Optimal Harvesting Policy ◽  
Commercial Importance

A dynamical model is proposed and analyzed to discuss the effect of population on a resource biomass by taking into account the crowding effect. It is assumed that the resource biomass, which has commercial importance, is subjected to harvesting. The harvesting effort is assumed to be a dynamical variable and taxation is being used as a control variable. The optimal harvesting policy is discussed using the Pontryagin’s maximum principle.

Optimal harvesting of a spatially distributed renewable resource with endogenous pricing

2019 ◽  
Vol 14 (1) ◽  
pp. 101
Author(s):  
S. Anita ◽  
S. Behringer ◽  
A.-M. Mosneagu ◽  
T. Upmann
Keyword(s):  
Optimality Conditions ◽  
Iterative Algorithm ◽  
Necessary Optimality Conditions ◽  
Renewable Resource ◽  
Optimal Harvesting ◽  
Spatially Distributed

In this paper, we focus on the exploitation of a renewable resource in a spatial setting. Building upon the spatial harvesting model of [Behringer and Upmann, J. Econ. Dyn. Control 42 (2014) 105–120], we endogenize the price for the resource assuming that after harvesting the good is non-durable, i.e. the harvesting yield must be supplied on the market instantaneously. We find necessary optimality conditions and use them to derive an iterative algorithm to improve at each step the harvesting effort. We find that with endogenous prices the full exploitation result of [Behringer and Upmann, J. Econ. Dyn. Control 42 (2014) 105–120] may cease to hold.

Water as a Blessing and a Transient Resource: A Call to Re-Define Modern Attitudes towards Water in Light of Job 14:7–12

2018 ◽  
Vol 26 (2) ◽  
Author(s):  
Jonathan Kivatsi Kavusa
Keyword(s):  
Human Life ◽  
Renewable Resource ◽  
Dead Tree ◽  
Responsible Management ◽  
The Earth ◽  
Metaphor Theory ◽  
Bodies Of Water ◽  
Ecological Potential

This article explores the ecological potential in Job 14:7–12. The metaphor in Job 14 praises the life-giving potential of water to revive a dead tree before presenting its transient character, similar to human life. The article investigates the question of why the author of Job finds it appropriate to use water and water-related images to contrast the potential of water to revive a dead tree with the transient mortals who disappear at death like great bodies of water in times of drought. Using elements of historical, critical, and literary approaches, as well as metaphor theory, and applying the Earth Bible Principle of intrinsic worth, this article argues that water should not be viewed as a limitlessly renewable resource, but a precious gift requiring responsible management.

Verdichten mit «Greening», oder was wir von Singapur lernen können (Essay)

2015 ◽  
Vol 166 (4) ◽  
pp. 219-222
Author(s):  
Urs Gantner
Keyword(s):  
Agricultural Land ◽  
Renewable Resource ◽  
Popular Participation ◽  
Botanical Gardens ◽  
Living Space ◽  
Urban Neighbourhoods ◽  
Mixed Use ◽  
City State ◽  
Vertical Greening ◽  
The City

Densification by greening, or what we can learn from Singapore (essay) Singapore, a city-state with a high population density, wants to give its population, its tourists and its economy a living and livable city and has developed the concept of the Garden City. Parks, nature reserves, forest, green corridors, trees, botanical gardens, horizontal and vertical greening of buildings, as well as popular participation, are all important for this vision of the city. Singapore is counting on dense construction alongside “greening” and biodiversity. Let us be prepared to learn from Singapore's example! Our land is also a non-renewable resource. To protect our ever more limited agricultural land, we should renounce any extension of building land, and free ourselves from the expanding carpets of suburban development. Let us build multiple urban neighbourhoods with mixed use and more biodiversity. Let us develop new types of communal gardens. Urban gardens in the widest sense – from private gardens to garden cooperatives, to parks and botanical gardens – are a part of our living space. The city should be our garden.

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