scholarly journals Dynamical behaviors of a predator-prey system with prey impulsive diffusion and dispersal delay between two patches

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Haiyun Wan ◽  
Haining Jiang
Keyword(s):  
Predator Prey ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Impulsive Diffusion

scholarly journals Hopf bifurcation in a diffusive predator–prey model with Smith growth rate and herd behavior

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Heping Jiang ◽  
Huiping Fang ◽  
Yongfeng Wu
Keyword(s):  
Hopf Bifurcation ◽  
Neumann Boundary ◽  
Herd Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Prey Model ◽  
Homogeneous Neumann Boundary Condition ◽  
The Stability

Abstract This paper mainly aims to consider the dynamical behaviors of a diffusive delayed predator–prey system with Smith growth and herd behavior subject to the homogeneous Neumann boundary condition. For the analysis of the predator–prey model, we have studied the existence of Hopf bifurcation by analyzing the distribution of the roots of associated characteristic equation. Then we have proved the stability of the periodic solution by calculating the normal form on the center of manifold which is associated to the Hopf bifurcation points. Some numerical simulations are also carried out in order to validate our analysis findings. The implications of our analytical and numerical findings are discussed critically.

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.

Dynamical Behaviors for a Predator-Prey System with State-Dependent Impulsive Effects

2011 ◽  
Vol 130-134 ◽  
pp. 385-390
Author(s):  
Ling Zhen Dong ◽  
Lan Sun Chen
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Impulsive System ◽  
Impulsive Effects ◽  
Predator Prey ◽  
Dynamical Behaviors ◽  
Prey System ◽  
State Dependent ◽  
Impulsive Model

With some theory about continuous and impulsive dynamical system, an impulsive model based on a special predator-prey system is considered. We assume that the impulsive effects occur when the density of the prey reaches a given value. For such a state-dependent impulsive system, the existence, uniqueness and orbital asymptotic stability of an order-1 periodic solution are discussed. Further, the existence of an order-2 periodic solution is also obtained, and persistence of the system is investigated.

scholarly journals Dynamical behaviors in a discrete fractional-order predator-prey system

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5857-5874 ◽  
Author(s):  
Yao Shi ◽  
Qiang Ma ◽  
Xiaohua Ding
Keyword(s):  
Numerical Simulations ◽  
Fixed Points ◽  
Fractional Order ◽  
Control Strategies ◽  
Flip Bifurcation ◽  
Predator Prey ◽  
Local Asymptotic Stability ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Theoretical Results

This paper is related to the dynamical behaviors of a discrete-time fractional-order predatorprey model. We have investigated existence of positive fixed points and parametric conditions for local asymptotic stability of positive fixed points of this model. Moreover, it is also proved that the system undergoes Flip bifurcation and Neimark-Sacker bifurcation for positive fixed point. Various chaos control strategies are implemented for controlling the chaos due to Flip and Neimark-Sacker bifurcations. Finally, numerical simulations are provided to verify theoretical results. These results of numerical simulations demonstrate chaotic behaviors over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behaviors in the model.

Hopf Bifurcation of a Generalized Delay-Induced Predator–Prey System with Habitat Complexity

2020 ◽  
Vol 30 (06) ◽  
pp. 2050082
Author(s):  
Zhihui Ma
Keyword(s):  
Hopf Bifurcation ◽  
Habitat Complexity ◽  
Sufficient Conditions ◽  
Explicit Formulas ◽  
Predator Prey ◽  
Dynamical Behaviors ◽  
Prey System ◽  
The Stability ◽  
Theoretical Results ◽  
Positivity And Boundedness

A delay-induced nonautonomous predator–prey system with variable habitat complexity is proposed based on mathematical and ecological issues, and this system is more realistic than the published models. Firstly, the permanence of the nonautonomous predation system is studied and some sufficient conditions are obtained. Secondly, the dynamical behaviors of the corresponding autonomous predation system are investigated, including the positivity and boundedness, and local and global stabilities. Thirdly, the properties of Hopf bifurcation of the autonomous predation system without/with delay are investigated and the explicit formulas which determine the stability and the direction of periodic solutions are obtained. Finally, a numerical example is given to test our theoretical results.

A delayed predator–prey system with impulsive diffusion between two patches

2016 ◽  
Vol 10 (01) ◽  
pp. 1750010 ◽  
Author(s):  
Hong-Li Li ◽  
Long Zhang ◽  
Zhi-Dong Teng ◽  
Yao-Lin Jiang
Keyword(s):  
Time Delays ◽  
Impulsive Differential Equation ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Analysis Techniques ◽  
Prey System ◽  
Impulsive Diffusion ◽  
Population Interactions ◽  
Theoretical Results

In most models of population dynamics, diffusion between two patches is assumed to be either continuous or discrete. However, in the real world, it is often the case that diffusion occurs at certain moment every year, impulsive diffusion can provide a more suitable manner to model the actual dispersal (or migration) behaviors for many ecological species. In addition, it is generally recognized that some kinds of time delays are inevitable in population interactions. In view of these facts, a delayed predator–prey system with impulsive diffusion between two patches is proposed. By using comparison theorem of impulsive differential equation and some analysis techniques, criteria on the global attractivity of predator-extinction periodic solution are established, sufficient conditions for the permanence of system are obtained. Finally, numerical simulations are presented to illustrate our theoretical results.

scholarly journals Dynamical Behaviors of a Stage-Structured Predator-Prey Model with Harvesting Effort and Impulsive Diffusion

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Lingzhi Huang ◽  
Zhichun Yang
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Comparison Theorem ◽  
Discrete Dynamical System ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey Model ◽  
Impulsive Diffusion

We consider a delayed predator-prey model with harvesting effort and impulsive diffusion between two patches. By the impulsive comparison theorem and the discrete dynamical system determined by the stroboscopic map, we obtain some sufficient conditions on the existence and global attractiveness of predator-eradicated periodic solution for the system. Furthermore, the permanence of the system is derived. The obtained results will modify and improve the ones in some existing publications and give the estimate for the ultimately low and upper boundedness of the systems.

Dynamical behaviors of a partial-dependent predator–prey system☆

2006 ◽  
Vol 28 (1) ◽  
pp. 67-75 ◽  
Author(s):  
Zunshui Cheng ◽  
Yiping Lin ◽  
Jinde Cao
Keyword(s):  
Predator Prey ◽  
Dynamical Behaviors ◽  
Prey System
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