Flip bifurcation and stability analysis of a fractional-order population dynamics with Allee effect. Issue 6 (18th August 2019)

• Record Type: Journal Article
• Authors: Bozkurt, F.; Yousef, A.
• Is Part Of: Journal of interdisciplinary mathematics. Volume 22:Issue 6(2019)
• Page Start: 1009
• Page End: 1029
• Publication Date: 2019-08-18
• Subjects: 34A08 -- 34A12 -- 34D20; Fractional order differential equation -- Stability -- Existence, and Uniqueness -- Flip bifurcation -- Allee threshold; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.1080/09720502.2019.1698403
• Languages: English
• ISSNs: 0972-0502

Abstract

Abstract: In this paper, we established a fractional-order logistic model for a monoclonal brain tumor growth known as Glioblastoma (GB). We show at first that the model possesses non-negative solutions. Furthermore, we studied the stability, existence, and uniqueness of the constructed model. To investigate the case for the extinction of the tumor population, we consider the Allee threshold. By using the center manifold theorem and bifurcation theory, we show that the model undergoes flip bifurcation. The numerical results support the theoretical study.