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.

A MODEL FOR AN INSHORE-OFFSHORE FISHERY

2003 ◽  
Vol 11 (01) ◽  
pp. 27-41 ◽  
Author(s):  
B. DUBEY ◽  
P. SINHA ◽  
P. CHANDRA
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Local Stability ◽  
Optimal Harvesting ◽  
Discount Rates ◽  
Nonlinear Mathematical Model ◽  
Optimal Harvesting Policy ◽  
Fishery Resources ◽  
Control Instrument

In this paper, a nonlinear mathematical model to study the dynamics of an inshore-offshore fishery under variable harvesting is proposed and analyzed. Criteria for local stability, instability and global stability of the system are derived. The optimal harvesting policy is discussed by considering taxation as a control instrument. It is shown that the fishery resources can be protected from overexploitation by increasing the tax and discount rates.

scholarly journals Harvesting Model for Fishery Resource with Reserve Area and Bird Predator

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Amit Sharma ◽  
Bhanu Gupta
Keyword(s):  
Numerical Simulation ◽  
Maximum Principle ◽  
Global Stability ◽  
Local Stability ◽  
Optimal Harvesting ◽  
Fishery Resource ◽  
Reserve Area ◽  
Proposed Model ◽  
Stability And Instability ◽  
Theoretical Results

The aim of this paper is to study the dynamics of fishery resource with reserve area in the presence of bird predator. The aquatic region under investigation is divided into two zones: one free for fishing and another restricted for any kind of fishery. The criteria of biological and bionomic equilibrium of system are established. The points of local stability, global stability, and instability are obtained for the proposed model. An optimal harvesting policy is established using Pontryagin’s maximum principle. At last the theoretical results obtained are illustrated with the help of numerical simulation.

MANAGEMENT OF A PREY-PREDATOR FISHERY BASED ON CONTINUOUS FISHING EFFORT

2004 ◽  
Vol 12 (03) ◽  
pp. 301-313 ◽  
Author(s):  
T. K. KAR ◽  
U. K. PAHARI ◽  
K. S. CHAUDHURI
Keyword(s):  
Maximum Principle ◽  
Local Stability ◽  
Fishing Effort ◽  
Steady States ◽  
Dynamic Variable ◽  
Numerical Examples ◽  
Selective Harvesting ◽  
Control Instrument ◽  
Optimal Tax ◽  
Predator Model

This paper deals with the problem of selective harvesting in a hybrid type of prey-predator model. Here we have taken the fishing effort as a dynamic variable and tax as a control instrument. The existence of the possible steady states along with their local stability is discussed. The optimal tax policy is also discussed with the help of Pontryagin's maximum principle. Finally, two numerical examples are taken to illustrate some of the key results.

scholarly journals Dynamics and optimal Harvesting strategy for biological models with Beverton –Holt growth

2020 ◽  
pp. 223-232
Author(s):  
Oday Kassim Shalsh ◽  
Sadiq Al-Nassir
Keyword(s):  
Maximum Principle ◽  
Numerical Simulations ◽  
Dynamic Behavior ◽  
Mathematical Analysis ◽  
Local Stability ◽  
Discrete Models ◽  
Optimal Harvesting ◽  
Biological Models ◽  
Optimal Harvest ◽  
Harvest Strategy

In this work, the dynamic behavior of discrete models is analyzed with Beverton- Holt function growth . All equilibria are found . The existence and local stability are investigated of all its equilibria.. The optimal harvest strategy is done for the system by using Pontryagin’s maximum principle to solve the optimality problem. Finally numerical simulations are used to solve the optimality problem and to enhance the results of mathematical analysis

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.

A RESOURCE DEPENDENT FISHERY MODEL WITH OPTIMAL HARVESTING POLICY

2002 ◽  
Vol 10 (01) ◽  
pp. 1-13 ◽  
Author(s):  
BALRAM DUBEY ◽  
PEEYUSH CHANDRA ◽  
PRAWAL SINHA
Keyword(s):  
Single Species ◽  
Fish Population ◽  
Maximum Sustainable Yield ◽  
Equilibrium Density ◽  
Future Price ◽  
Optimal Harvesting ◽  
Biomass Density ◽  
Optimal Harvesting Policy ◽  
Yield Increase ◽  
Fishery Model

A dynamic model for a single-species fishery, which depends partially on a logistically growing resource with functional response, is proposed using taxation as control instrument to protect fish population from overexploitation. The analysis of the model shows that both the equilibrium density of fish population as well as the maximum sustainable yield increase as resource biomass density increases. The optimal harvesting policy is also discussed with the help of Pontryagin's Maximum Principle. It is found that for the optimum equilibrium value of resource biomass density, the total user's cost of harvest per unit effort must be equal to the discounted value of future price at the steady state.

OPTIMAL SHAPE OF A HEAVY ELASTIC ROD LOADED WITH A TIP-CONCENTRATED FORCE AGAINST LATERAL BUCKLING

2009 ◽  
Vol 09 (02) ◽  
pp. 383-390 ◽  
Author(s):  
BRANISLAVA N. NOVAKOVIC ◽  
TEODOR M. ATANACKOVIC
Keyword(s):  
Maximum Principle ◽  
Optimality Criterion ◽  
Pontryagin’S Maximum Principle ◽  
Optimal Shape ◽  
The Other ◽  
Lateral Stability ◽  
Elastic Rod ◽  
Lateral Buckling ◽  
Concentrated Force ◽  
Pontryagin's Maximum Principle

By using Pontryagin's maximum principle, we determine the optimal shape of an elastic rod free at one and clamped at the other. The rod is loaded with a concentrated force at the free end and its own weight. The optimality criterion is the volume of the rod guaranteeing lateral stability.

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