Stability and Bifurcation in a Predator–Prey Model with the Additive Allee Effect and the Fear Effect

Liyun Lai, Zhenliang Zhu and Fengde Chen
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Liyun Lai: College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China
Zhenliang Zhu: College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China
Fengde Chen: College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China

Mathematics, 2020, vol. 8, issue 8, 1-21

Abstract: We proposed and analyzed a predator–prey model with both the additive Allee effect and the fear effect in the prey. Firstly, we studied the existence and local stability of equilibria. Some sufficient conditions on the global stability of the positive equilibrium were established by applying the Dulac theorem. Those results indicate that some bifurcations occur. We then confirmed the occurrence of saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation. Those theoretical results were demonstrated with numerical simulations. In the bifurcation analysis, we only considered the effect of the strong Allee effect. Finally, we found that the stronger the fear effect, the smaller the density of predator species. However, the fear effect has no influence on the final density of the prey.

Keywords: fear effect; additive allee effect; saddle-node bifurcation; transcritical bifurcation; hopf bifucation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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