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.

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 Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II

2019 ◽  
Vol 6 (1) ◽  
pp. 1-17
Author(s):  
W. Abid ◽  
R. Yafia ◽  
M. A. Aziz-Alaoui ◽  
Ahmed Aghriche
Keyword(s):  
Existence Of Solutions ◽  
Optimal Harvesting ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Optimal Harvest ◽  
Predator Model ◽  
Maximal Principle ◽  
Theoretical Results ◽  
Optimal Harvest Policy

AbstractIn this work, we consider the optimal harvesting and stability problems of a prey-predator model with modified Leslie-Gower and Holling-type II functional response. The model is governed by a system of three differential equations which describe the interactions between prey, predator and harvesting effort. Boundedness and existence of solutions for this system are showed. The existence and local stability of the possible steady states are analyzed and the conditions of global stability of the interior equilibrium are established by using the Lyapunov function, we prove also the occurrence of Hopf bifurcation at this point. By using the Pontryagin’s maximal principle, we formulate and we solve the problem of the optimal harvest policy. In the end, some numerical simulations are given to support our theoretical results.

Optimal harvesting of a prey–predator model with variable carrying capacity

2017 ◽  
Vol 10 (05) ◽  
pp. 1750069 ◽  
Author(s):  
Chaity Ganguli ◽  
T. K. Kar ◽  
P. K. Mondal
Keyword(s):  
Carrying Capacity ◽  
Intraspecific Competition ◽  
Dynamical Behavior ◽  
Optimal Harvesting ◽  
Main Concern ◽  
Interior Equilibrium ◽  
Optimal Harvest ◽  
Common Resource ◽  
Predator Model ◽  
Optimal Harvest Policy

This work deals with a prey–predator model in an environment where the carrying capacities are assumed to be variable with time and one species feeds upon the other. Independent harvesting efforts are applied in either species and asymmetrical intraguild predation occurs. A common resource is consumed by two competing species and at the same time predator also consumes the prey. At first we discuss the model under constant carrying capacity and make the conclusion that no limit cycle exists in this case. Then we discuss the model without intraspecific competition. Our main concern is to cover the above mentioned two cases together, i.e. the model with variable carrying capacity and intraspecific competition. We determine the steady states and examine the dynamical behavior. We also analyze the local and global stability of the interior equilibrium by Routh–Hurwitz criterion and a suitable Lyapunov function respectively. A Hopf bifurcation occurs with respect to a parameter which is the ratio of predator’s and prey’s intrinsic growth rate. The possibility of bionomic equilibrium has been considered. The optimal harvest policy is formulated and solved with Pontryagin’s maximum principle. Some numerical simulations are given to explain most of the analytical results.

scholarly journals Analysis of a Fishery Model with two competing prey species in the presence of a predator species for Optimal Harvesting

2018 ◽  
Vol 31 ◽  
pp. 08008 ◽  
Author(s):  
Sutimin ◽  
Siti Khabibah ◽  
Dita Anis Munawwaroh
Keyword(s):  
Ecological Model ◽  
Dynamical Behavior ◽  
Fish Population ◽  
Optimal Harvesting ◽  
Globally Asymptotically Stable ◽  
Predator Species ◽  
Optimal Harvest ◽  
The Stability ◽  
Fishery Model ◽  
Maximal Principle

A harvesting fishery model is proposed to analyze the effects of the presence of red devil fish population, as a predator in an ecosystem. In this paper, we consider an ecological model of three species by taking into account two competing species and presence of a predator (red devil), the third species, which incorporates the harvesting efforts of each fish species. The stability of the dynamical system is discussed and the existence of biological and bionomic equilibrium is examined. The optimal harvest policy is studied and the solution is derived in the equilibrium case applying Pontryagin’s maximal principle. The simulation results is presented to simulate the dynamical behavior of the model and show that the optimal equilibrium solution is globally asymptotically stable. The results show that the optimal harvesting effort is obtained regarding to bionomic and biological equilibrium.

scholarly journals Dynamics of the Stochastic Belousov-Zhabotinskii Chemical Reaction Model

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 663
Author(s):  
Ying Yang ◽  
Daqing Jiang ◽  
Donal O’Regan ◽  
Ahmed Alsaedi
Keyword(s):  
Chemical Reaction ◽  
Existence And Uniqueness ◽  
Reaction Model ◽  
Equation Model ◽  
Asymptotically Stable ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Globally Asymptotically Stable ◽  
Chemical Reaction Model ◽  
Theoretical Results

In this paper, we discuss the dynamic behavior of the stochastic Belousov-Zhabotinskii chemical reaction model. First, the existence and uniqueness of the stochastic model’s positive solution is proved. Then we show the stochastic Belousov-Zhabotinskii system has ergodicity and a stationary distribution. Finally, we present some simulations to illustrate our theoretical results. We note that the unique equilibrium of the original ordinary differential equation model is globally asymptotically stable under appropriate conditions of the parameter value f, while the stochastic model is ergodic regardless of the value of f.

Bioeconomic Modelling of a Single Species Fishery with Gompertz Law of Growth

1998 ◽  
Vol 06 (04) ◽  
pp. 393-409 ◽  
Author(s):  
T. Pradhan ◽  
K. S. Chaudhuri
Keyword(s):  
Dynamic Control ◽  
Control Variable ◽  
Single Species ◽  
Fishing Effort ◽  
Catch Per Unit Effort ◽  
Bioeconomic Modelling ◽  
Optimal Harvest ◽  
Gompertz Law ◽  
Fishery Model ◽  
Optimal Harvest Policy

A single species fishery model has been developed using the Gompertz law of population growth and the CPUE (Catch-per-unit-effort) hypothesis. The dynamical and the bionomic steady states were determined and their natures were examined from the biological as well as economic view points. The optimal harvest policy is discussed by taking the fishing effort as a dynamic control variable. The results are compared with those of the Schaefer model [10].

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