CAPITAL THEORETIC ANALYSIS OF A HOLLING–TANNER-TYPE PREY–PREDATOR FISHERY WITH TAXATION AS A CONTROL INSTRUMENT

2009 ◽  
Vol 02 (02) ◽  
pp. 151-165
Author(s):  
TAPASI DAS ◽  
R. N. MUKHERJEE ◽  
K. S. CHAUDHURI
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Reaction Model ◽  
Fishing Effort ◽  
Dynamic Interaction ◽  
Optimal Harvesting ◽  
Theoretic Analysis ◽  
Dynamic Reaction ◽  
Dynamic Variable ◽  
Control Instrument

The level of fishing effort expands or contracts in a dynamic reaction model of a fishery accordingly as the net economic revenue (i.e. perceived rent) to the fishermen is positive or negative. A dynamic reaction model reflects this dynamic interaction between the perceived rent and the effort in a fishery. The combined harvesting of a prey–predator fishery is assumed to be regulated by an external authority by imposing a tax per unit biomass of both the species. The fishing effort is taken to be a dynamic variable of time, which is proportional to the instantaneous capital invested in the fishery. The steady states of the system along with their local as well as global stability are considered. The optimal harvesting policy with the tax as a control instrument is discussed. The results are numerically discussed and graphically illustrated. Sensitivity analysis of the parameters is carried out. The paper ends with concluding remarks.

REGULATION OF A PREY-PREDATOR FISHERY BY TAXATION: A DYNAMIC REACTION MODEL

2003 ◽  
Vol 11 (02) ◽  
pp. 173-187 ◽  
Author(s):  
T. K. KAR ◽  
K. S. CHAUDHURI
Keyword(s):  
Dynamical System ◽  
Prey Species ◽  
Social Benefit ◽  
Reaction Model ◽  
Fishing Effort ◽  
Dynamic Interaction ◽  
Theoretic Approach ◽  
Dynamic Reaction ◽  
Growth Equations ◽  
Gross Rate

In a fully dynamic model of an open-access fishery, the level of fishery effort expands or contracts according as the net economic revenue (i.e., perceived rent) to the fisherman is positive or negative. A model reflecting this dynamic interaction between the perceived rent and the effort in a fishery, is called a dynamic reaction model. In this paper, we study a dynamic reaction model, in which the prey species is subjected to harvesting in the presence of a predator and a tax. It is also assumed that the gross rate of investment of capital in the fishery is proportional to the perceived rent. With this capital theoretic approach, the dynamical system consisting of the growth equations of the two species and also of the fishing effort is formulated. The steady state is determined and its stability is discussed. The object is to maximize the monetary social benefit as well as prevent the predator from extinction, keeping the ecological balance.

scholarly journals A Dynamic Model for Fishery Resource with Reserve Area and Taxation

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hai-Feng Huo ◽  
Hui-Min Jiang ◽  
Xin-You Meng
Keyword(s):  
Fish Population ◽  
Reaction Model ◽  
Dynamic Reaction ◽  
Fishery Resource ◽  
Control Instrument ◽  
Optimal Harvest ◽  
Over Exploitation ◽  
Theoretical Results ◽  
Resource System ◽  
Optimal Harvest Policy

The present paper deals with a dynamic reaction model of a fishery. The dynamics of a fishery resource system in an aquatic environment consists of two zones: a free fishing zone and a reserve zone. To protect fish population from over exploitation, a control instrument tax is imposed. The existence of its steady states and their stability are studied. The optimal harvest policy is discussed next with the help of Pontryagin's maximum principle. Our theoretical results are confirmed by numerical simulation.

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.

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 A dynamic reaction model of an inshore-offshore fishery with taxation as a control instrument

2014 ◽  
Vol 10 (4) ◽  
pp. 13-20
Author(s):  
Jayjayanti Ray ◽  
◽  
Tarun Pradhan
Keyword(s):  
Reaction Model ◽  
Dynamic Reaction ◽  
Control Instrument

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

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