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 Effects of Over-Harvesting and Drought on a Predator-Prey System with Optimal Control

2018 ◽  
Vol 08 (08) ◽  
pp. 459-482 ◽  
Author(s):  
Alanus Mapunda ◽  
Eunice Mureithi ◽  
Nyimvua Shaban ◽  
Thadei Sagamiko
Keyword(s):  
Optimal Control ◽  
Predator Prey ◽  
Prey System

scholarly journals About an optimal control for a "predator-prey" system

2020 ◽  
pp. 287-294
Author(s):  
S.V. Pashko ◽  
Keyword(s):  
Optimal Control ◽  
Phase Space ◽  
Differential Equations ◽  
Stationary Point ◽  
Optimal Trajectories ◽  
Limit Case ◽  
Control Variables ◽  
Predator Prey ◽  
Phase Trajectories ◽  
Prey System

We consider the system of Lotka-Volterra differential equations with two control variables and describe an optimal control, which provides a transition to a stationary point in a minimum time. We also found an optimal control for the limit case, on condition that the phase trajectories are located near a stationary point. Optimal trajectories of motion in the phase space are constructed; they look like spirals.

Existence and Uniqueness for Stochastic Predator-Prey System of Two Species with Age-Structured

2011 ◽  
Vol 219-220 ◽  
pp. 680-684
Author(s):  
Fei Fei Li ◽  
Qi Min Zhang
Keyword(s):  
Strong Solution ◽  
Existence And Uniqueness ◽  
Population System ◽  
Predator Prey ◽  
Prey System ◽  
Age Dependent ◽  
Age Structured

In this paper we introduce a stochastic age-dependent predator-prey system. Existence and uniqueness of strong solution for a stochastic population system of two species with age-dependent are proved. The analysis uses Barkholder-Davis-Gundy’s inequality,ItÔ's formula and some special inequalities to achieve our purpose.

scholarly journals Hopf bifurcation and optimal control in a diffusive predator-prey system with time delay and prey harvesting

2012 ◽  
Vol 17 (4) ◽  
pp. 379-409 ◽  
Author(s):  
Xiaoyuan Chang ◽  
Junjie Wei
Keyword(s):  
Optimal Control ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Functional Differential Equations ◽  
Normal Form Theory ◽  
Flux Boundary Condition ◽  
Predator Prey ◽  
Prey System ◽  
Functional Differential ◽  
The Stability

In this paper, we investigated the dynamics of a diffusive delayed predator-prey system with Holling type II functional response and nozero constant prey harvesting on no-flux boundary condition. At first, we obtain the existence and the stability of the equilibria by analyzing the distribution of the roots of associated characteristic equation. Using the time delay as the bifurcation parameter and the harvesting term as the control parameter, we get the existence and the stability of Hopf bifurcation at the positive constant steady state. Applying the normal form theory and the center manifold argument for partial functional differential equations, we derive an explicit formula for determining the direction and the stability of Hopf bifurcation. Finally, an optimal control problem has been considered.

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