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.

scholarly journals Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Caifeng Du
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

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 Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Guodong Liu ◽  
Xiaohong Wang ◽  
Xinzhu Meng ◽  
Shujing Gao
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Persistence In Mean ◽  
Predator Prey Model ◽  
Prey System ◽  
Delay Differential ◽  
Lévy Jumps

In this paper, we explore an impulsive stochastic infected predator-prey system with Lévy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.

scholarly journals Permanence for a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jiangbin Chen ◽  
Shengbin Yu
Keyword(s):  
Feedback Control ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Control Variables ◽  
Predator Prey ◽  
Type Iii ◽  
Prey System ◽  
Ratio Dependent

A new set of sufficient conditions for the permanence of a ratio-dependent predator-prey system with Holling type III functional response and feedback controls are obtained. The result shows that feedback control variables have no influence on the persistent property of the system, thus improving and supplementing the main result of Yang (2008).

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 Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited

2013 ◽  
Vol 2013 ◽  
pp. 1-19
Author(s):  
Denis de Carvalho Braga ◽  
Luis Fernando Mello ◽  
Antonio Carlos Zambroni de Souza
Keyword(s):  
Differential Equations ◽  
Bifurcation Diagram ◽  
Periodic Orbits ◽  
Vector Fields ◽  
Predator Prey ◽  
Codimension Two ◽  
Prey System ◽  
Made In

The main goal of this paper is to present a theory of approximation of periodic orbits of vector fields in the plane. From the theory developed here, it is possible to obtain an approximation to the curve of nonhyperbolic periodic orbits in the bifurcation diagram of a family of differential equations that has a transversal Hopf point of codimension two. Applications of the developed theory are made in Liénard-type equations and in Bazykin’s predator-prey system.

scholarly journals Analysis of an Impulsive Predator-Prey System with Monod-Haldane Functional Response and Seasonal Effects

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Hunki Baek ◽  
Younghae Do ◽  
Yasuhisa Saito
Keyword(s):  
Differential Equations ◽  
Functional Response ◽  
Impulsive Differential Equations ◽  
Seasonal Effects ◽  
Predator Prey ◽  
Prey System

For a class of impulsive predator-prey systems with Monod-Haldane functional response and seasonal effects, we investigate conditions for the local and global stabilities of prey-free solutions and for the permanence of the system by using the Flquet theory of impulsive differential equations and comparison techniques. In addition, we numerically analyze the phenomena caused by seasonal effects and impulsive perturbation. It will be applicable to the controllability for the population of prey and predator.

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