Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect

Abstract

We analyze the dynamics of a fractional order modified Leslie-Gower model with Beddington-DeAngelis functional response and additive Allee effect by means of local stability. In this respect, all possible equilibria and their existence conditions are determined and their stability properties are established. We also construct nonstandard numerical schemes based on Grünwald-Letnikov approximation. The constructed scheme is explicit and maintains the positivity of solutions. Using this scheme, we perform some numerical simulations to illustrate the dynamical behavior of the model. It is noticed that the nonstandard Grünwald-Letnikov scheme preserves the dynamical properties of the continuous model, while the classical scheme may fail to maintain those dynamical properties.

The Influence of Additive Allee Effect and Periodic Harvesting to the Dynamics of Leslie-Gower Predator-Prey Model

“…One interesting phenomenon in ecological modeling is the Allee effect, which represents the decrease in per capita fertility rate as a result of several mechanisms such as lowdensity population, intraspecific competition, and difficulties in finding mates [7] [8]. Several researchers using different definitions to represents the Allee effect in a predatorprey model such as multiplicative Allee effect [9][10], additive Allee effect [11]- [13], and double Allee effect [14] [15].…”

“…The flow of solutions of system(7) with parameter values as in eq. (16)and = 0.2, = 0.1, ℎ = 0., the numerical solution of system (7) when the Allee effect is weak is demonstrated.…”

Stability and bifurcation in a single species logistic model with additive Allee effect and feedback control

“…For example, in [23], the authors presented the Hopf bifurcation and stability analysis for a delayed logistic equation with additive Allee effect. Moreover, the predator-prey model, the diffusive or the impulsive ecological model, the fractional order Leslie-Gower model, and the hybrid bioeconomic system with the additive Allee effect were investigated in [24][25][26][27][28][29][30][31], and [32], respectively.…”

Dynamics of eco-epidemiological model with harvesting

“…Recently, many researches have proposed the various versions of Leslie Gower by using Allee effect, various functional response, on fractional order, etc., see e.g. [10][11][12][13].…”