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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. (C) 2019 Elsevier Ltd. All rights reserved.
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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
ISSN: 1468-1218
Year: 2019
Volume: 48
Page: 71-93
2 . 0 7 2
JCR@2019
1 . 8 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
ESI HC Threshold:59
JCR Journal Grade:1
CAS Journal Grade:2
Cited Count:
WoS CC Cited Count: 48
SCOPUS Cited Count: 57
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1
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