Stability and Bifurcation Analysis of an Amensalism Model with Weak Allee Effect

In this paper, an amensalism model with weak Allee effect is proposed. The existence and stability of all possible positive equilibria and the possible boundary equilibria of the system are investigated. We also prove that there are two saddle-node bifurcations under suitable conditions by Sotomayor...

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Bibliographic Details
Published inQualitative theory of dynamical systems Vol. 19; no. 1
Main Authors Wei, Zhen, Xia, Yonghui, Zhang, Tonghua
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2020
Springer Nature B.V
Subjects
Bifurcation theory
Computer simulation
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Stability analysis
Amensalism model
34C25
Stability
92D25
34D20
34D40
Week Allee effect
Saddle-node bifurcation
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ISSN1575-5460
1662-3592
DOI10.1007/s12346-020-00341-0

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Summary:In this paper, an amensalism model with weak Allee effect is proposed. The existence and stability of all possible positive equilibria and the possible boundary equilibria of the system are investigated. We also prove that there are two saddle-node bifurcations under suitable conditions by Sotomayor’s theorem. An example with its numeric simulations are given to verify our main results.
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ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-020-00341-0