Dynamical analysis of a two species amensalism model with Beddington–DeAngelis functional response and Allee effect on the second species. (August 2019)

• Record Type: Journal Article
• Authors: Guan, Xinyu; Chen, Fengde
• Is Part Of: Nonlinear analysis. Volume 48(2019)
• Page Start: 71
• Page End: 93
• Publication Date: 2019-08
• Subjects: Amensalism model -- Beddington–DeAngelis functional response -- Allee effect -- Bifurcation -- Global dynamics; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.01.002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A two species amensalism model with Beddington–DeAngelis functional response is proposed and studied in this paper. The existence and stability of possible equilibria are investigated. Under some additional assumptions, there are two stable equilibria which implies this system is not asymptotically stable. Based on the stability analysis of equilibria, closed orbits and the saddle connection, we give some comprehensive bifurcation and global dynamics of the system. Next, we further incorporate the Allee effect into the second species and provide a complete qualitative and bifurcation analysis of the system with Allee effect. Numerical simulations show that the system with an Allee effect must take a longer time to reach its stable steady-state solution than that without Allee effect. There is a good agreement between the present results and the numeric simulations.