Optimal control for an age-dependent predator-prey system in a polluted environment

2013 ◽  
Vol 44 (1-2) ◽  
pp. 491-509 ◽  
Author(s):  
Zhixue Luo
Keyword(s):  
Optimal Control ◽  
Polluted Environment ◽  
Predator Prey ◽  
Prey System ◽  
Age Dependent

scholarly journals Optimal control of harvesting for age-dependent predator-prey system

2005 ◽  
Vol 42 (5-6) ◽  
pp. 573-584 ◽  
Author(s):  
Chun Zhao ◽  
Miansen Wang ◽  
Ping Zhao
Keyword(s):  
Optimal Control ◽  
Predator Prey ◽  
Prey System ◽  
Age Dependent

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.

Dynamics and Optimal Control of a Monod–Haldane Predator–Prey System with Mixed Harvesting

2020 ◽  
Vol 30 (16) ◽  
pp. 2050243
Author(s):  
Xinxin Liu ◽  
Qingdao Huang
Keyword(s):  
Optimal Control ◽  
Periodic Solution ◽  
Local Stability ◽  
Maximum Yield ◽  
Multiple Shooting ◽  
Boundedness Of Solutions ◽  
Predator Prey ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Nontrivial Periodic Solution

This paper investigates the dynamics and optimal control of the Monod–Haldane predator–prey system with mixed harvesting that combines both continuous and impulsive harvestings. The periodic solution of the prey-free is studied and the local stability condition is obtained. The boundedness of solutions, the permanence of the system, and the existence of nontrivial periodic solution are studied. With the change of parameters, the system appears with a stable nontrivial periodic solution when the prey-free periodic solution loses stability. Numerical simulations show that the system has complex dynamical behaviors via bifurcation diagrams. Further, the maximum yield problem of the harvested system is studied, which is transformed into a nonlinear programming problem and solved by the method of combined multiple shooting and collocation.

scholarly journals Mathematical and numerical analysis for Predator-prey system in a polluted environment

2010 ◽  
Vol 5 (4) ◽  
pp. 813-847 ◽  
Author(s):  
Verónica Anaya ◽  
◽  
Mostafa Bendahmane ◽  
Mauricio Sepúlveda ◽  
◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Polluted Environment ◽  
Predator Prey ◽  
Prey System

scholarly journals Modelling a predator–prey system with infected prey in polluted environment

2010 ◽  
Vol 34 (7) ◽  
pp. 1861-1872 ◽  
Author(s):  
Sudipa Sinha ◽  
O.P. Misra ◽  
J. Dhar
Keyword(s):  
Polluted Environment ◽  
Predator Prey ◽  
Prey System ◽  
Infected Prey

scholarly journals Analysis of Stochastic Delay Predator-Prey System with Impulsive Toxicant Input in Polluted Environments

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Meng Liu
Keyword(s):  
Polluted Environment ◽  
Stochastic Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Time Average

A stochastic delay predator-prey model in a polluted environment with impulsive toxicant input is proposed and studied. The thresholds between stability in time average and extinction of each population are obtained. Some recent results are extended and improved greatly. Several simulation figures are introduced to support the conclusions.

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