scholarly journals Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity

2018 ◽  
Vol 73 ◽  
pp. 06001
Author(s):  
Anies Munawwaroh Dita ◽  
Sutimin ◽  
Khabibah Siti
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Prey Density ◽  
Optimal Harvesting ◽  
Limited Effect ◽  
Sustainable Harvesting ◽  
Bionomic Equilibrium ◽  
Maximal Principle ◽  
Coexistence Equilibrium ◽  
Biological Equilibrium

We proposed a model of prey-predator fishing by considering proportion of prey density and toxicity in ecosystem. The model is analysed to study about biological equilibrium, bionomic equilibrium and its stability. The aim of the model is to determine the optimal sustainable harvesting for each species. The optimal harvesting is resulted from Pontryagin’s maximal principle. The global stability of coexistence equilibrium is analyzed from Lyapunov function. The effect of toxicity leads to the decreasing of sustainable harvesting.

scholarly journals Harvesting of a Single-Species System Incorporating Stage Structure and Toxicity

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Huiling Wu ◽  
Fengde Chen
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Optimal Policy ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Single Species ◽  
Structured Model ◽  
Bionomic Equilibrium ◽  
Maximal Principle

A single species stage-structured model incorporating both toxicant and harvesting is proposed and studied. It is shown that toxicant has no influence on the persistent property of the system. The existence of the bionomic equilibrium is also studied. After that, we consider the system with variable harvest effect; sufficient conditions are obtained for the global stability of bionomic equilibrium by constructing a suitable Lyapunov function. The optimal policy is also investigated by using Pontryagin's maximal principle. Some numeric simulations are carried out to illustrate the feasibility of the main results. We end this paper by a brief discussion.

scholarly journals Analysis of optimal harvesting of a prey-predator fishery model with the limited sources of prey and presence of toxicity

2018 ◽  
Vol 73 ◽  
pp. 06018
Author(s):  
Sutimin ◽  
Khabibah Siti ◽  
Anies Munawwaroh Dita
Keyword(s):  
Prey Density ◽  
Equilibrium Points ◽  
Optimal Harvesting ◽  
Predator Species ◽  
Existence Of Equilibrium ◽  
Sustainable Harvesting ◽  
Toxicity Factor ◽  
The Stability ◽  
Fishery Model ◽  
Coexistence Equilibrium

A model of prey and predator species is discussed to study the effects of the limited prey density and presence of toxicity. The model is studied for sustainable optimal harvesting. The existence of equilibrium points is analyzed to find the stability of coexistence equilibrium, and use Pontryagin’s maximal method to obtain the sustainable optimal harvesting. The results show that the optimal harvesting is obtained from the solution of optimal equilibrium. The toxicity factor decreases the sustainable harvesting.

scholarly journals Harvesting in a two-prey one-predator fishery: a bioeconomic model

2004 ◽  
Vol 45 (3) ◽  
pp. 443-456 ◽  
Author(s):  
T. K. Kar ◽  
K. S. Chaudhuri
Keyword(s):  
Lyapunov Function ◽  
Prey Density ◽  
Feeding Rate ◽  
Bioeconomic Model ◽  
Numerical Examples ◽  
The Third ◽  
Optimal Harvest ◽  
Predator Response ◽  
Maximal Principle ◽  
Optimal Harvest Policy

AbstractA multispecies harvesting model with interference is proposed. The model is based on Lotka-Volterra dynamics with two competing species which are affected not only by harvesting but also by the presence of a predator, the third species. In order to understand the dynamics of this complicated system, we choose to model the simplest possible predator response function in which the feeding rate of the predator increases linearly with prey density. We derive the conditions for global stability of the system using a Lyapunov function. The possibility of existence of a bioeconomic equilibrium is discussed. The optimal harvest policy is studied and the solution is derived in the equilibrium case using Pontryagin's maximal principle. Finally, some numerical examples are discussed.

scholarly journals Qualitative properties of mathematical model of English language education

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Atena Ghasemabadi ◽  
Nahid Soltanian
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Equilibrium Point ◽  
English Language ◽  
Language Education ◽  
Qualitative Properties ◽  
English Language Education ◽  
Compound Matrices ◽  
Reproduction Numbers ◽  
Coexistence Equilibrium

AbstractThis paper presents a mathematical model that examines the impacts of traditional and modern educational programs. We calculate two reproduction numbers. By using the Chavez and Song theorem, we show that backward bifurcation occurs. In addition, we investigate the existence and local and global stability of boundary equilibria and coexistence equilibrium point and the global stability of the coexistence equilibrium point using compound matrices.

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.

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 Permanence and global stability of positive solutions of a nonautonomous discrete ratio-dependent predator-prey model

2005 ◽  
Vol 2005 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Positive Solution ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

We first give sufficient conditions for the permanence of nonautonomous discrete ratio-dependent predator-prey model. By linearization of the model at positive solutions and construction of Lyapunov function, we also obtain some conditions which ensure that a positive solution of the model is stable and attracts all positive solutions.

scholarly journals On Global Stability of Disease-Free Equilibrium in Epidemiological Models

2021 ◽  
Vol 2 (3) ◽  
pp. 37-42
Author(s):  
Tunde Tajudeen Yusuf
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Direct Approach ◽  
Epidemiological Models ◽  
Homogeneous Population ◽  
Disease Free

This paper considers the problem of constructing appropriate Lyapunov function for establishing the global stability of a disease-free equilibrium in epidemiological models. A generalised algorithm is proposed and it is tested for some selected epidemiological models. Experience from the application of the algorithm on test examples shows that the algorithm is easy to use, less cumbersome, and yielded the desired result, particularly in models with homogeneous population. Thus, the proposed algorithm provides a direct approach for establishing global stability of disease-free equilibrium.

scholarly journals Mathematical Model for Impact of Media on Cleanliness Drive in India

2018 ◽  
Vol 7 (1) ◽  
pp. 29-36
Author(s):  
N H Shah ◽  
J S Patel ◽  
F A Thakkar ◽  
M H Satia
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lyapunov Function ◽  
Global Stability ◽  
Transfer Rate ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Local And Global Stability

A mathematical model on cleanliness drive in India is analysed for active cleaners and passive cleaners. Cleanliness and endemic equilibrium points are found. Local and global stability of these equilibrium points are discussed using Routh-Hurwitz criteria and Lyapunov function respectively. Impact of media (as a control) is studied on passive cleaners to become active. Numerical simulation of the model is carried out which indicates that with the help of media transfer rate to active cleaners from passive cleaners is higher.

Sign in / Sign up

Export Citation Format

Share Document