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Can I read Modelling the Dynamics in a Predator–Prey System with Allee Effects and Anti-predator Behavior on EtoBox?
Modelling the Dynamics in a Predator–Prey System with Allee Effects and Anti-predator Behavior by Tao Wen; Yancong Xu; Mu He; Libin Rong is a Mathematics article available to read on EtoBox.
What is Modelling the Dynamics in a Predator–Prey System with Allee Effects and Anti-predator Behavior about?
This paper studies a predator-prey model with strong and weak Allee effects and anti-predator behavior using a dynamical system approach. We perform a detailed bifurcation analysis including saddle-node bifurcation, Hopf bifurcation of codimension 3, cusp of codimension 3, cusp type Bogdanov-Takens bifurcation of codimension 3, and codimension-2 cusp of the limit cycle. The involvement of strong and weak Allee effects provides a new regime shift mechanism, which indicates the transition from a homoclinic cycle to a new heteroclinic cycle connecting two boundary equilibria induced by the Allee effect and the carrying capacity. The role of anti-predator behavior is fully uncovered by studying the interaction with the Allee effect. It is the first time that we find a codimension-2 cusp of infinitesimal limit cycle in the predatorprey system, which indicates the existence of a coexistence region of three limit cycles due to the weak Allee effect. Different from the scenario in the reference (Aguirre et al. in SIAM J Appl Math 69(5): [1244][1245][1246][1247][1248][1249][1250][1251][1252][1253][1254][1255][1256][1257][1258][1259][1260][1261][1262] 2009), it is a new generating mechanism
Who reads Modelling the Dynamics in a Predator–Prey System with Allee Effects and Anti-predator Behavior?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Tao Wen; Yancong Xu; Mu He; Libin Rong
- Publisher
- Springer Science and Business Media LLC
- Published
- 2023
- Language
- EN
- Field
- Mathematics (Physical Sciences)