A predator-prey system with two impulses on the diseased prey and a Beddington-DeAngelis response

Wang, Xia; Song, Xinyu

doi:10.1002/mma.1169

Cited by 2 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on some experimental data, some researchers proposed different types of functional responses such as Holling types , Sigmoidal and Freedman (Table ). It is worth noting that many useful results on the dynamical behavior of biological system with a specific functional response can be found in . However, most of these studies are restricted to the numerical analysis and neglect the effect of seasonality.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior for a class of predator–prey system with general functional response and discontinuous harvesting policy

Cai

Huang

Zhang

et al. 2015

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we introduce a class of predator-prey system with general functional response, whose harvesting policy is modeled by a discontinuous function. Based on the differential inclusions theory, topological degree theory in set-valued analysis and generalized Lyapunov approach, we analyze the existence, uniqueness and global asymptotic stability of positive periodic solution. In particular, a series of useful criteria on existence, uniqueness and global asymptotic stability of the positive equilibrium point are established for the autonomous system corresponding to the non-autonomous biological and mathematical model with a discontinuous right-hand side. Moreover, some new sufficient conditions are provided to guarantee the global convergence in measure of harvesting solution and convergence in finite time of any positive solution for the autonomous discontinuous biological system. The obtained results, which improve and generalize previous works on dynamical behavior in the literature, are of interest for understanding and designing biological system with not only continuous or even Lipschitz continuous but also discontinuous harvesting function. Finally, we give three examples with numerical simulations to show the applicability and effectiveness of our main results.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamical behavior for a class of predator–prey system with general functional response and discontinuous harvesting policy

Cai

Huang

Zhang

et al. 2015

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate

Wang¹,

Guo²,

Song³

2011

Comput. Appl. Math.

Self Cite

View full text Add to dashboard Cite

Abstract. In this paper, we consider the pest management model with spraying microbial pesticide and releasing the infected pests, and the infected pests have the function similar to the microbial pesticide and can infect the healthy pests, further weaken or disable their prey function till death. By using the Floquet theory for impulsive differential equations, we show that there exists a globally asymptotically stable pest eradication periodic solution when the impulsive period τ < τ max , we further prove that the system is uniformly permanent if the impulsive period τ > τ max . Finally, by means of numerical simulation, we show that with the increase of impulsive period, the system displays complicated behaviors.Mathematical subject classification: 34C05, 92D25.

show abstract

A predator-prey system with two impulses on the diseased prey and a Beddington-DeAngelis response

Cited by 2 publications

References 11 publications

Dynamical behavior for a class of predator–prey system with general functional response and discontinuous harvesting policy

Dynamical behavior for a class of predator–prey system with general functional response and discontinuous harvesting policy

Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate

Contact Info

Product

Resources

About