Stability analysis and optimal harvesting policy of prey-predator model with stage structure for predator

2014 ◽  
Vol 8 ◽  
pp. 7923-7934 ◽  
Author(s):  
Syamsuddin Toaha ◽  
Jeffry Kusuma ◽  
Khaeruddin ◽  
Mawardi Bahri
Keyword(s):  
Stability Analysis ◽  
Stage Structure ◽  
Optimal Harvesting ◽  
Optimal Harvesting Policy ◽  
Predator Model

scholarly journals Optimal harvesting policy of a prey–predator model with Crowley–Martin-type functional response and stage structure in the predator

2018 ◽  
Vol 23 (4) ◽  
pp. 493-514 ◽  
Author(s):  
Balram Dubey ◽  
Shikhar Agarwal ◽  
Ankit Kumar
Keyword(s):  
Three Dimensional ◽  
Stage Structure ◽  
Optimal Level ◽  
Effective Control ◽  
Optimal Harvesting ◽  
Catch Per Unit Effort ◽  
Optimal Harvesting Policy ◽  
Control Instrument ◽  
Long Time ◽  
Predator Model

In this paper, a three-dimensional dynamical model consisting of a prey, a mature predator, and an immature predator is proposed and analysed. The interaction between prey and mature predator is assumed to be of the Crowley–Martin type, and both the prey and mature predator are harvested according to catch-per-unit-effort (CPUE) hypothesis. Steady state of the system is obtained, stability analysis (local and global both) are discussed to explore the long-time behaviour of the system. The optimal harvesting policy is also discussed with the help of Pontryagin's maximum principle. The harvesting effort is taken as an effective control instrument to preserve prey and predator and to maintain them at an optimal level.

STABILITY AND BIFURCATION ANALYSIS OF A DISCRETE PREY–PREDATOR MODEL WITH SQUARE-ROOT FUNCTIONAL RESPONSE AND OPTIMAL HARVESTING

2020 ◽  
Vol 28 (01) ◽  
pp. 91-110
Author(s):  
PRABIR CHAKRABORTY ◽  
UTTAM GHOSH ◽  
SUSMITA SARKAR
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Functional Response ◽  
Population Model ◽  
Optimal Harvesting ◽  
Herd Behavior ◽  
Square Root ◽  
Optimal Harvesting Policy ◽  
Optimal Value ◽  
Predator Model

In this paper, we have considered a discrete prey–predator model with square-root functional response and optimal harvesting policy. This type of functional response is used to study the dynamics of the prey–predator model where the prey population exhibits herd behavior, i.e., the interaction between prey and predator occurs along the boundary of the population. The considered population model has three fixed points; one is trivial, the second one is axial and the last one is an interior fixed point. The first two fixed points are always feasible but the last one depends on the parameter value. The interior fixed point experiences the flip and Neimark–Sacker bifurcations depending on the predator harvesting coefficient. Finally, an optimal harvesting policy has been introduced and the optimal value of the harvesting coefficient is determined.

scholarly journals Dynamics of a Harvested Prey–Predator Model with Prey Refuge Dependent on Both Species

2018 ◽  
Vol 28 (12) ◽  
pp. 1830040 ◽  
Author(s):  
Md. Manarul Haque ◽  
Sahabuddin Sarwardi
Keyword(s):  
Limit Cycle ◽  
Optimal Harvesting ◽  
Present System ◽  
Prey Refuge ◽  
Bionomic Equilibrium ◽  
Optimal Harvesting Policy ◽  
Equilibrium Level ◽  
Main Observation ◽  
Predator Model

The present paper deals with a prey–predator model with prey refuge in proportion to both species, and the independent harvesting of each species. Our study shows that using refuge as control, it can break the limit cycle of the system and reach the required state of equilibrium level. We have established the optimal harvesting policy. The boundedness, feasibility of interior equilibria and bionomic equilibrium have been determined. The main observation is that the coefficient of refuge plays an important role in regulating the dynamics of the present system. Moreover, the variation of the coefficient of refuge changes the system from stable to unstable and vice-versa. Some numerical illustrations are given in order to support our analytical and theoretical findings.

scholarly journals Stability Analysis of a Harvested Prey-Predator Model with Stage Structure and Maturation Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Liu ◽  
Qingling Zhang ◽  
James Huang
Keyword(s):  
Stability Analysis ◽  
Stage Structure ◽  
Model System ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Maturation Delay ◽  
Effort Level ◽  
Selective Harvest ◽  
Proposed Model ◽  
Predator Model

A harvested prey-predator model with density-dependent maturation delay and stage structure for prey is proposed, where selective harvest effort on predator population is considered. Conditions which influence positiveness and boundedness of solutions of model system are analytically investigated. Criteria for existence of all equilibria and uniqueness of positive equilibrium are also studied. In order to discuss effects of maturation delay and harvesting on model dynamics, local stability analysis around all equilibria of the proposed model system is discussed due to variation of maturation delay and harvest effort level. Furthermore, global stability of positive equilibrium is investigated by utilizing an iterative technique. Finally, numerical simulations are carried out to show consistency with theoretical analysis.

scholarly journals Dynamics and Optimal Taxation Control in a Bioeconomic Model with Stage Structure and Gestation Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Yi Zhang ◽  
Qingling Zhang ◽  
Fenglan Bai
Keyword(s):  
Optimal Taxation ◽  
Stable Limit Cycle ◽  
Stage Structure ◽  
Model System ◽  
Optimal Harvesting ◽  
Stable Limit ◽  
Gestation Delay ◽  
Interior Equilibrium ◽  
Control Instrument ◽  
Predator Model

A prey-predator model with gestation delay, stage structure for predator, and selective harvesting effort on mature predator is proposed, where taxation is considered as a control instrument to protect the population resource in prey-predator biosystem from overexploitation. It shows that interior equilibrium is locally asymptotically stable when the gestation delay is zero, and there is no periodic orbit within the interior of the first quadrant of state space around the interior equilibrium. An optimal harvesting policy can be obtained by virtue of Pontryagin's Maximum Principle without considering gestation delay; on the other hand, the interior equilibrium of model system loses as gestation delay increases through critical certain threshold, a phenomenon of Hopf bifurcation occurs, and a stable limit cycle corresponding to the periodic solution of model system is also observed. Finally, numerical simulations are carried out to show consistency with theoretical analysis.

Nonlinear Dynamics of a Prey–Predator Model Using Precise and Imprecise Harvesting Phenomena with Biological Parameters

2017 ◽  
Vol 12 (02) ◽  
pp. 39-68 ◽  
Author(s):  
S. Vijaya ◽  
E. Rekha ◽  
J. Jayamal Singh
Keyword(s):  
Nonlinear Dynamics ◽  
Stability Analysis ◽  
Numerical Experiments ◽  
Optimal Harvesting ◽  
Biological Parameters ◽  
Predator Species ◽  
Biological Phenomena ◽  
Predator Model ◽  
The Stability ◽  
Parameter Values

This paper presents the nonlinear dynamics of a one-prey and one-predator harvesting model with precise in nature as well as imprecise in biological phenomena parameters. We derived the conditions for boundedness, the equilibrium point, and stability analysis. Both precise and imprecise models showed stable, unstable, and saddle-point states. The stability analysis revealed the existence of biological and bionomic equilibria. In this study, we found the optimal harvesting policy for both prey and predator species. Finally, numerical experiments were performed with various parameter values to observe the variation of equilibrium states.

DYNAMICAL BEHAVIOR OF A HARVESTED PREY-PREDATOR MODEL WITH STAGE STRUCTURE AND DISCRETE TIME DELAY

2009 ◽  
Vol 17 (04) ◽  
pp. 759-777 ◽  
Author(s):  
CHAO LIU ◽  
QINGLING ZHANG ◽  
JAMES HUANG ◽  
WANSHENG TANG
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Dynamical Behavior ◽  
Stage Structure ◽  
Model System ◽  
Optimal Harvesting ◽  
Gestation Delay ◽  
Interior Equilibrium ◽  
Discrete Time Delay ◽  
Predator Model

A prey-predator model with stage structure for prey and selective harvest effort on predator is proposed, in which gestation delay is considered and taxation is used as a control instrument to protect the population from overexploitation. It is established that when the discrete time delay is zero, the model system is stable around the interior equilibrium and an optimal harvesting policy is discussed with the help of Pontryagin's maximum principle; On the other hand, stability switch of the model system due to the variation of discrete time delay is also studied, which reveals that the discrete time delay has a destabilizing effect. As the discrete time delay increases through a certain threshold, a phenomenon of Hopf bifurcation occurs and a limit cycle corresponding to the periodic solution of model system is also observed. Numerical simulations are carried out to show the consistency with theoretical analysis.

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