Permanence of a stage-structured predator–prey system

Chen, Fengde; Chen, Wanlin; Wu, Yuanchao; Ma, Zhihui

doi:10.1016/j.amc.2013.03.055

Cited by 34 publications

(30 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, the research work on the permanence of predator-prey systems with delay-dependent parameters is scare. One can see [3,6,7,21,27].…”

Section: Introductionmentioning

confidence: 99%

Permanence of a Two Species Delayed Competitive Model With Stage Structure and Harvesting

Xu¹,

Zu²

2015

Bulletin of the Korean Mathematical Society

View full text Add to dashboard Cite

Abstract. In this paper, a two species competitive model with stage structure and harvesting is investigated. By using the differential inequality theory, some new sufficient conditions which ensure the permanence of the system are established. Our result supplements the main results of Song and Chen [Global asymptotic stability of a two species competitive system with stage structure and harvesting, Commun. Nonlinear Sci. Numer. Simul. 19 (2001), 81-87].

show abstract

“…Recently, the research work on the permanence of predator-prey systems with delay-dependent parameters is scare. One can see [3,6,7,21,27].…”

Section: Introductionmentioning

confidence: 99%

Permanence of a Two Species Delayed Competitive Model With Stage Structure and Harvesting

Xu¹,

Zu²

2015

Bulletin of the Korean Mathematical Society

View full text Add to dashboard Cite

show abstract

“…The predator-prey model is one of the basic models between different species in nature which has been widely researched [1][2][3][4][5][6]. In the natural world, the population generally has a saturation effect.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation in a Holling type II predator–prey model with Allee effect and time delay

2018

View full text Add to dashboard Cite

In this paper, we consider a Holling type II predator-prey model incorporating time delay and Allee effect in prey. We discuss the influence of Allee effect on the logistic equation. By analyzing the characteristic equation of the corresponding linearized system, we give the threshold condition for the local asymptotic stability of the system according to the change of birth rate or Allee effect in prey. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. In addition, we show that if the Allee effect is large or the birth rate is small, then both predators and prey are extinct. The Allee effect can influence the stability of the system.

show abstract

“…This assumption seems not be realistic for most, if not all, animals and insects. In the real world, there are many species whose individuals have a life history that takes them through two stages, immature and mature, where immatures are raised by their parents, and the rate they attack at prey and the reproductive rate can be ignored (see, for example, [8,10,15,17,18]). …”

Section: Introductionmentioning

confidence: 99%

A stage-structured predator–prey model with distributed maturation delay and harvesting

Al-Omari

2015

Journal of Biological Dynamics

View full text Add to dashboard Cite

A stage-structured predator-prey system with distributed maturation delay and harvesting is investigated. General birth and death functions are used. The local stability of each feasible equilibria is discussed. By using the persistence theory, it is proven that the system is permanent if the coexistence equilibrium exists. By using Lyapunov functional and LaSalle invariant principle, it is shown that the trivial equilibrium is globally stable when the other equilibria are not feasible, and that the boundary equilibrium is globally stable if the coexistence equilibrium does not exist. Finally, sufficient conditions are derived for the global stability of the coexistence equilibrium. ARTICLE HISTORY

show abstract

Permanence of a stage-structured predator–prey system

Cited by 34 publications

References 13 publications

Permanence of a Two Species Delayed Competitive Model With Stage Structure and Harvesting

Permanence of a Two Species Delayed Competitive Model With Stage Structure and Harvesting

Stability and bifurcation in a Holling type II predator–prey model with Allee effect and time delay

A stage-structured predator–prey model with distributed maturation delay and harvesting

Contact Info

Product

Resources

About