Dynamics of a predator–prey model with double Allee effects and impulse

Liu, Xiangsen; Dai, Binxiang

doi:10.1007/s11071-016-3270-7

Cited by 10 publications

(2 citation statements)

References 33 publications

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“…Moreover, the effect is called to be a weak Allee effect if the density at zero per capita growth is positive, a strong Allee effect if the low-density per capita growth is negative. In the past decades, the Allee effect has always been introduced to explain some important biological phenomena by many mathematicians and ecologists [16][17][18][19][20][21][22][23][24][25]. It was shown that the low density population can affect the birth rate of the species [26], but the coefficients of the growth rate are irrelevant to the Allee-type function.…”

Section: Introductionmentioning

confidence: 99%

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

2018

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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.

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Section: Introductionmentioning

confidence: 99%

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

2018

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“…It is obvious that it is not at all evident to construct a mathematical model that will fit entirely any natural population interactions. In the literature, several models for predator-prey's systems have been already proposed and analyzed incorporating some specific effects (Bürger et al, 2017;Elettreby et al, 2017;Li et al, 2017aLi et al, , 2017bLiu et al, 2017Liu and Dai;Liu and Wiang, 2018;Yuan et al, 2018;Zhang et al, 2017a). The first proposed one was the Lotka Volterra predator-prey model (Volterra, 1928).…”

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confidence: 99%

Circuit Design and Experimental Investigations for a Predator–Prey Model

Saad

Hmidet

Boubaker

2018

International Journal on Smart Sensing and Intelligent Systems

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In recent years, dynamical relationship between species in ecology has been intensively investigated and will continue to be one of the most significant themes. The dynamics of predator-prey's systems are at the heart of these studies. Such models are generally depicted by nonlinear polynomials and exhibit many complex nonlinear phenomena. In this paper, not only a prey-predator model displaying richer dynamical behaviors is analyzed but also its electronic circuit is also designed via the MultiSIM software proving the very good agreement between biological theory considerations and electronic experiments.

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