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.

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.

Stability and Bifurcation of a Fishery Model with Crowley–Martin Functional Response

2017 ◽  
Vol 27 (11) ◽  
pp. 1750174 ◽  
Author(s):  
Atasi Patra Maiti ◽  
B. Dubey
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Equilibrium Points ◽  
Control Variable ◽  
Dynamical Variable ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Fishery Model

To understand the dynamics of a fishery system, a nonlinear mathematical model is proposed and analyzed. In an aquatic environment, we considered two populations: one is prey and another is predator. Here both the fish populations grow logistically and interaction between them is of Crowley–Martin type functional response. It is assumed that both the populations are harvested and the harvesting effort is assumed to be dynamical variable and tax is considered as a control variable. The existence of equilibrium points and their local stability are examined. The existence of Hopf-bifurcation, stability and direction of Hopf-bifurcation are also analyzed with the help of Center Manifold theorem and normal form theory. The global stability behavior of the positive equilibrium point is also discussed. In order to find the value of optimal tax, the optimal harvesting policy is used. To verify our analytical findings, an extensive numerical simulation is carried out for this model system.

MODELING AND ANALYSIS OF A HARVESTING FISHERY MODEL IN A TWO-PATCH ENVIRONMENT

2008 ◽  
Vol 01 (03) ◽  
pp. 287-298 ◽  
Author(s):  
LIMING CAI ◽  
XUEZHI LI ◽  
XINYU SONG
Keyword(s):  
Maximum Principle ◽  
Global Stability ◽  
Local Stability ◽  
Pontryagin’S Maximum Principle ◽  
Steady States ◽  
The Other ◽  
Optimal Harvesting ◽  
Modeling And Analysis ◽  
Optimal Harvesting Policy ◽  
Fishery Model

In this paper, a harvesting fishery model in a two-patch environment: one free-fishing zone and the other one reserved zone where fishing is strictly prohibited, is proposed and analyzed. The existence of possible biological steady states, along with their local stability, instability and global stability is discussed. The existence of bioeconomic equilibrium is derived. An optimal harvesting policy is also given by applying pontryagin's maximum principle.

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 Maximum Principle for Stochastic Recursive Optimal Control Problems Involving Impulse Controls

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhen Wu ◽  
Feng Zhang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Linear Quadratic ◽  
Regular Control

We consider a stochastic recursive optimal control problem in which the control variable has two components: the regular control and the impulse control. The control variable does not enter the diffusion coefficient, and the domain of the regular controls is not necessarily convex. We establish necessary optimality conditions, of the Pontryagin maximum principle type, for this stochastic optimal control problem. Sufficient optimality conditions are also given. The optimal control is obtained for an example of linear quadratic optimization problem to illustrate the applications of the theoretical results.

Harvesting Analysis of a Predator-Prey System with Functional Response

2013 ◽  
Vol 805-806 ◽  
pp. 1957-1961
Author(s):  
Ting Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Prey System ◽  
The Stability ◽  
Maximal Principle

In this paper, a predator-prey system with functional response is studied,and a set of sufficient conditions are obtained for the stability of equilibrium point of the system. Moreover, optimal harvesting policy is obtained by using the maximal principle,and numerical simulation is applied to illustrate the correctness.

Optimal harvesting for a single-species population governed by Gompertz law: Influence of environmental fluctuation and limited harvesting capacity

2019 ◽  
Vol 12 (02) ◽  
pp. 1950018
Author(s):  
P. D. N. Srinivasu ◽  
Simon D. Zawka
Keyword(s):  
Control Variable ◽  
Optimal Solution ◽  
Single Species ◽  
Optimal Harvesting ◽  
Environmental Fluctuation ◽  
Gompertz Equation ◽  
Species Population ◽  
Gompertz Law ◽  
Binding Constraints ◽  
Single Species Population

This work presents an optimal harvesting problem associated with a single-species population governed by Gompertz law in a seasonally fluctuating environment. The influence of environmental fluctuation is accommodated by choosing the coefficients in the differential equation to be periodic functions with the same period and restriction on the harvesting effort is accommodated by considering binding constraints on the control variable. Hence, a linear optimal control problem has been considered where the state dynamics is governed by Gompertz equation and the control variable is subject to the binding constraints. With the help of maximum principle and the concept of blocked intervals, an optimal periodic solution has been obtained which is followed by the construction of optimal solution using the theory of most rapid approach. Important results of the study are demonstrated through numerical simulations.

OPTIMAL HARVESTING OF FISHING AQUACULTURE IN THE ENVIRONMENT WITH PRYMNESIACEE TOXIN

2016 ◽  
Vol 24 (02n03) ◽  
pp. 237-255 ◽  
Author(s):  
SHUANGHONG ZHANG ◽  
QINGLING ZHANG ◽  
CHAO LIU
Keyword(s):  
Maximum Principle ◽  
Finite Time ◽  
Silver Carp ◽  
Bighead Carp ◽  
Optimal Harvesting ◽  
Time Stability ◽  
Finite Time Stability ◽  
Harvesting Method ◽  
Pollutant Source ◽  
The Pontryagin Maximum Principle

In this paper, the issue on the optimal harvesting of fish catching after eliminating toxin during the fish aquaculture is studied. Taking the aquaculture of bighead carp and silver carp as an example, considering the characteristics of the growth and the reproduction of prymnesiacee, and taking prymnesiacee toxin as the pollutant source, a harvesting model of fish aquaculture is built. The finite-time stability of the system is discussed. While the fish aquaculture and the elimination of the algae toxin targeted as pollutant source can be carried out simultaneously, an optimal harvesting method is made by the Pontryagin maximum principle, from which a general algorithm of the optimal harvesting solution can be obtained. The stimulation shows the effectiveness of the result.

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