scholarly journals Optimal harvesting policy of a stochastic delay predator-prey model with Lévy jumps

2017 ◽  
Vol 10 (08) ◽  
pp. 4222-4230
Author(s):  
Meiling Deng
Keyword(s):  
Optimal Harvesting ◽  
Stochastic Delay ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Predator Prey Model ◽  
Prey Model ◽  
Lévy Jumps

scholarly journals Dynamic Behaviors of a Harvesting Leslie-Gower Predator-Prey Model

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Na Zhang ◽  
Fengde Chen ◽  
Qianqian Su ◽  
Ting Wu
Keyword(s):  
Sufficient Conditions ◽  
Practical Significance ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Predator Species ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Predator Prey Model ◽  
Prey Model ◽  
Suitable Restriction

A Leslie-Gower predator-prey model incorporating harvesting is studied. By constructing a suitable Lyapunov function, we show that the unique positive equilibrium of the system is globally stable, which means that suitable harvesting has no influence on the persistent property of the harvesting system. After that, detailed analysis about the influence of harvesting is carried out, and an interesting finding is that under some suitable restriction, harvesting has no influence on the final density of the prey species, while the density of predator species is strictly decreasing function of the harvesting efforts. For the practical significance, the economic profit is considered, sufficient conditions for the presence of bionomic equilibrium are given, and the optimal harvesting policy is obtained by using thePontryagin'smaximal principle. At last, an example is given to show that the optimal harvesting policy is realizable.

The stage-structured predator–prey model and optimal harvesting policy

2000 ◽  
Vol 168 (2) ◽  
pp. 201-210 ◽  
Author(s):  
Xin-an Zhang ◽  
Lansun Chen ◽  
Avidan U Neumann
Keyword(s):  
Optimal Harvesting ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Optimal Harvesting Policy of Predator-Prey Model with Free Fishing and Reserve Zones

2017 ◽  
Author(s):  
Syamsuddin Toaha ◽  
Rustam Rustam
Keyword(s):  
Equilibrium Point ◽  
Optimal Harvesting ◽  
Present Value ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Maximum Profit ◽  
Prey Model ◽  
Net Revenue

If any question related to this paper, please ask via [email protected]. This article is an INA-Rxiv post-print post from the OSF (Open Science Framework) which is self-archiving. This article has been presented on SYMPOSIUM ON BIOMATHEMATICS (SYMOMATH 2016) and its proceedings are published in AIP Conference Proceedings, Volume 1825, Issue 1 with links http://aip.scitation.org/doi/abs/10.1063/1.4978992The present paper deals with an optimal harvesting of predator-prey model in an ecosystem that consists of two zones, namely the free fishing and prohibited zones. The dynamics of prey population in the ecosystem can migrate from the free fishing to the prohibited zone and vice versa. The predator and prey populations in the free fishing zone are then harvested with constant efforts. The existence of the interior equilibrium point is analyzed and its stability is determined using Routh-Hurwitz stability test. The stable interior equilibrium point is then related to the problem of maximum profit and the problem of present value of net revenue. We follow the Pontryagin’s maximal principle to get the optimal harvesting policy of the present value of the net revenue. From the analysis, we found a critical point of the efforts that makes maximum profit. There also exists certain conditions of the efforts that makes the present value of net revenue becomes maximal. In addition, the interior equilibrium point is locally asymptotically stable which means that the optimal harvesting is reached and the unharvested prey, harvested prey, and harvested predator populations remain sustainable. Numerical examples are given to verify the analytical results.

Bifurcation Analysis and Optimal Harvesting of a Delayed Predator–Prey Model

2015 ◽  
Vol 25 (01) ◽  
pp. 1550012 ◽  
Author(s):  
P. Tchinda Mouofo ◽  
R. Djidjou Demasse ◽  
J. J. Tewa ◽  
M. A. Aziz-Alaoui
Keyword(s):  
Natural Resource Management ◽  
Optimal Control Theory ◽  
Uniform Boundedness ◽  
Optimal Harvesting ◽  
Global Dynamics ◽  
Saddle Node Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Local Bifurcations ◽  
Prey Model

A delay predator–prey model is formulated with continuous threshold prey harvesting and Holling response function of type III. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The positive invariance of the non-negative orthant is proved and the uniform boundedness of the trajectories. Stability of equilibria is investigated and the existence of some local bifurcations is established: saddle-node bifurcation, Hopf bifurcation. We use optimal control theory to provide the correct approach to natural resource management. Results are also obtained for optimal harvesting. Numerical simulations are given to illustrate the results.

Local Bifurcations and Optimal Theory in a Delayed Predator–Prey Model with Threshold Prey Harvesting

2015 ◽  
Vol 25 (07) ◽  
pp. 1540015 ◽  
Author(s):  
Israel Tankam ◽  
Plaire Tchinda Mouofo ◽  
Abdoulaye Mendy ◽  
Mountaga Lam ◽  
Jean Jules Tewa ◽  
...  
Keyword(s):  
Time Delay ◽  
Piecewise Linear ◽  
Optimal Harvesting ◽  
Threshold Policy ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Local Bifurcations ◽  
Prey Model ◽  
Linear Threshold ◽  
The Stability

We investigate the effects of time delay and piecewise-linear threshold policy harvesting for a delayed predator–prey model. It is the first time that Holling response function of type III and the present threshold policy harvesting are associated with time delay. The trajectories of our delayed system are bounded; the stability of each equilibrium is analyzed with and without delay; there are local bifurcations as saddle-node bifurcation and Hopf bifurcation; optimal harvesting is also investigated. Numerical simulations are provided in order to illustrate each result.

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