Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect. (28th May 2017)

• Record Type: Journal Article
• Authors: Suryanto, Agus; Darti, Isnani; Anam, Syaiful
• Other Names: Kalla Shyam L. Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2017(2017)
• Publication Date: 2017-05-28
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2017/8273430
• Languages: English
• ISSNs: 0161-1712

Abstract

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.