Optimal harvesting for a stochastic Lotka-Volterra predator-prey system with jumps and nonselective harvesting hypothesis

2015 ◽  
Vol 37 (4) ◽  
pp. 641-662 ◽  
Author(s):  
Xiaoling Zou ◽  
Ke Wang
Keyword(s):  
Optimal Harvesting ◽  
Predator Prey ◽  
Prey System ◽  
Nonselective Harvesting

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.

scholarly journals Dynamics and optimal harvesting of a stochastic predator-prey system with regime switching, S-type distributed time delays and Lévy jumps

2021 ◽  
Vol 7 (3) ◽  
pp. 4068-4093
Author(s):  
Yuanfu Shao ◽  
Keyword(s):  
Regime Switching ◽  
Time Delays ◽  
Optimal Harvesting ◽  
Comparison Theory ◽  
Predator Prey ◽  
Prey System ◽  
Persistence In The Mean ◽  
Distributed Time Delays ◽  
Stability In Distribution ◽  
Lévy Jumps

<abstract><p>This work is concerned with a stochastic predator-prey system with S-type distributed time delays, regime switching and Lévy jumps. By use of the stochastic differential comparison theory and some inequality techniques, we study the extinction and persistence in the mean for each species, asymptotic stability in distribution and the optimal harvesting effort of the model. Then we present some simulation examples to illustrate the theoretical results and explore the effects of regime switching, distributed time delays and Lévy jumps on the dynamical behaviors, respectively.</p></abstract>

scholarly journals Hopf Bifurcation Analysis of a Predator-Prey Biological Economic System with Nonselective Harvesting

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Biwen Li ◽  
Zhenwei Li ◽  
Boshan Chen ◽  
Gan Wang
Keyword(s):  
Hopf Bifurcation ◽  
Economic System ◽  
Bifurcation Analysis ◽  
Economic Perspective ◽  
Modified Model ◽  
Bifurcation Theorem ◽  
Predator Prey ◽  
Economic Profit ◽  
Prey System ◽  
Nonselective Harvesting

A modified predator-prey biological economic system with nonselective harvesting is investigated. An important mathematical feature of the system is that the economic profit on the predator-prey system is investigated from an economic perspective. By using the local parameterization method and Hopf bifurcation theorem, we analyze the Hopf bifurcation of the proposed system. In addition, the modified model enriches the database for the predator-prey biological economic system. Finally, numerical simulations illustrate the effectiveness of our results.

OPTIMAL CONTROL FOR A PREDATOR-PREY SYSTEM WITH AGE-DEPENDENT

2009 ◽  
Vol 02 (01) ◽  
pp. 45-59 ◽  
Author(s):  
ZHIXUE LU
Keyword(s):  
Optimal Control ◽  
Existence And Uniqueness ◽  
Normal Cone ◽  
Optimal Harvesting ◽  
Negative Solution ◽  
Optimal Control Strategy ◽  
Predator Prey ◽  
Prey System ◽  
Age Dependent ◽  
Existence Of Optimal Control

This paper is concerned with optimal harvesting policy for predator-prey system of three species with age-dependent. The existence and uniqueness of non-negative solution of the system are proved using the fixed pint theorem. The existence of optimal control strategy is discussed, optimality conditions are derived by means of normal cone and Dubovitskii–Milyutin's general theory. Our results extend some known criteria.

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