REGULATION OF A PREY–PREDATOR FISHERY INCORPORATING PREY REFUGE BY TAXATION: A DYNAMIC REACTION MODEL

2011 ◽  
Vol 19 (03) ◽  
pp. 417-445 ◽  
Author(s):  
KUNAL CHAKRABORTY ◽  
MILON CHAKRABORTY ◽  
T. K. KAR
Keyword(s):  
Optimal Taxation ◽  
Social Benefit ◽  
Reaction Model ◽  
Fishing Effort ◽  
Model System ◽  
Prey Refuge ◽  
Predator Species ◽  
Taxation Policy ◽  
Proposed Model ◽  
Fishery Model

This paper, describes a prey–predator fishery model incorporating prey refuge. The proposed model reflecting the dynamic interaction between the net economic revenue and the fishing effort used to harvest the prey species in the presence of predation and a suitable tax. The steady states of the system are determined and the dynamic behavior of the model system is discussed. The occurrence of Hopf bifurcation of the proposed model system is examined through considering density-dependent mortality for the predator as bifurcation parameter. The optimal taxation policy is formulated and solved with the help of Pontryagin's maximal principle. The objective of the paper is to maximize the monetary social benefit as well as prevent the predator species from extinction, keeping the ecological balance. Results are illustrated with the help of numerical examples.

Analysis of Prey-Predator Three Species Fishery Model with Harvesting Including Prey Refuge and Migration

2016 ◽  
Vol 26 (02) ◽  
pp. 1650022 ◽  
Author(s):  
Sankar Kumar Roy ◽  
Banani Roy
Keyword(s):  
Fishing Effort ◽  
Predator Population ◽  
Prey Refuge ◽  
Resource Rent ◽  
Interior Equilibrium ◽  
Dynamic Framework ◽  
Resource Sustainability ◽  
And Migration ◽  
Fishery Model ◽  
Type Ii Functional Response

In this article, a prey-predator system with Holling type II functional response for the predator population including prey refuge region has been analyzed. Also a harvesting effort has been considered for the predator population. The density-dependent mortality rate for the prey, predator and super predator has been considered. The equilibria of the proposed system have been determined. Local and global stabilities for the system have been discussed. We have used the analytic approach to derive the global asymptotic stabilities of the system. The maximal predator per capita consumption rate has been considered as a bifurcation parameter to evaluate Hopf bifurcation in the neighborhood of interior equilibrium point. Also, we have used fishing effort to harvest predator population of the system as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent is earned from the resource. Finally, we have presented some numerical simulations to verify the analytic results and the system has been analyzed through graphical illustrations.

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.

Free Trade versus Protection : Static and Dynamic Aspects

1985 ◽  
Vol 24 (1) ◽  
pp. 39-50
Author(s):  
Gunnar Flфystad
Keyword(s):  
Developing Countries ◽  
Foreign Trade ◽  
Trade Policy ◽  
Empirical Evidence ◽  
Free Trade ◽  
Optimal Taxation ◽  
Foreign Trade Policy ◽  
Taxation Policy

This paper analyses whether the developing countries are pursuing an optimal foreign trade policy, given the theoretical and empirical evidence we have. The paper concludes that constraints in imposing other taxes than tariffs in many developing countries may justify having tariffs as part of an optimal taxation policy.

scholarly journals Dynamical analysis of a predator-prey interaction model with time delay and prey refuge

2018 ◽  
Vol 5 (1) ◽  
pp. 138-151 ◽  
Author(s):  
Jai Prakash Tripathi ◽  
Swati Tyagi ◽  
Syed Abbas
Keyword(s):  
Hopf Bifurcation ◽  
Functional Differential Equations ◽  
Interaction Model ◽  
Dynamical Analysis ◽  
Prey Refuge ◽  
Normal Form Theory ◽  
Predator Species ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Predator Prey Model

AbstractIn this paper, we study a predator-prey model with prey refuge and delay. We investigate the combined role of prey refuge and delay on the dynamical behaviour of the delayed system by incorporating discrete type gestation delay of predator. It is found that Hopf bifurcation occurs when the delay parameter τ crosses some critical value. In particular, it is shown that the conditions obtained for the Hopf bifurcation behaviour are sufficient but not necessary and the prey reserve is unable to stabilize the unstable interior equilibrium due to Hopf bifurcation. In particular, the direction and stability of bifurcating periodic solutions are determined by applying normal form theory and center manifold theorem for functional differential equations. Mathematically, we analyze the effect of increase or decrease of prey reserve on the equilibrium states of prey and predator species. At the end, we perform some numerical simulations to substantiate our analytical findings.

Kinetic study on the generation of furosine and pyrraline in a Maillard reaction model system of d-glucose and l-lysine

2020 ◽  
Vol 317 ◽  
pp. 126458 ◽  
Author(s):  
Hang Yu ◽  
Qili Zhong ◽  
Yunfei Xie ◽  
Yahui Guo ◽  
Yuliang Cheng ◽  
...  
Keyword(s):  
Kinetic Study ◽  
Maillard Reaction ◽  
Reaction Model ◽  
Model System

scholarly journals Hopf bifurcation and stability in a Beddington-DeAngelis predator-prey model with stage structure for predator and time delay incorporating prey refuge

2019 ◽  
Vol 17 (1) ◽  
pp. 141-159 ◽  
Author(s):  
Zaowang Xiao ◽  
Zhong Li ◽  
Zhenliang Zhu ◽  
Fengde Chen
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Bifurcation And Stability

Abstract In this paper, we consider a Beddington-DeAngelis predator-prey system with stage structure for predator and time delay incorporating prey refuge. By analyzing the characteristic equations, we study the local stability of the equilibrium of the system. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. After that, by constructing a suitable Lyapunov functional, sufficient conditions are derived for the global stability of the system. Finally, the influence of prey refuge on densities of prey species and predator species is discussed.

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.

scholarly journals Determination of Acrylamide Formed in Asparagine/d-Glucose Maillard Model Systems by Using Gas Chromatography with Headspace Solid-Phase Microextraction

2006 ◽  
Vol 89 (1) ◽  
pp. 149-153 ◽  
Author(s):  
Ahmed H El-Ghorab ◽  
Kazutoshi Fujioka ◽  
Takayuki Shibamoto
Keyword(s):  
Gas Chromatography ◽  
Maillard Reaction ◽  
Solid Phase Microextraction ◽  
Solid Phase ◽  
Reaction Model ◽  
Model System ◽  
Model Systems ◽  
Headspace Solid Phase Microextraction ◽  
Nitrogen Phosphorus

Abstract A gas chromatographic method, along with a headspace solid-phase microextraction (HS-SPME), was developed for the determination of acrylamide formed in Maillard reaction model systems. The developed method was validated by liquid chromatography/mass spectrometry. A headspace sample was collected from an aqueous acrylamide solution (100 μg/mL) by SPME and directly injected into a gas chromatograph equipped with a nitrogen-phosphorus detector. The recovery of acrylamide from an aqueous solution was satisfactory, i.e, >93% under the conditions used. Acrylamide formed in an asparagine/d-glucose (molar ratio, 1/2) Maillard reaction model system heated at 150 and 170C for 20 min was collected and analyzed by the newly developed method using gas chromatography with nitrogen-phosphorus detection and HS-SPME. The amounts of acrylamide were 318 33 μg/g asparagine from a sample heated at 150C and 3329 176 g/g asparagine from a sample heated at 170C. Addition of cysteamine or glutathione to the above model system reduced acrylamide formation. Acrylamide formation was not observed when cysteamine or glutathione was added to asparagine in the above model systems to obtain equimolar concentrations of both compounds. This newly developed method is simple and sensitive, and requires no solvent extraction.

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