Journal of Mathematical Biology

, Volume 62, Issue 3, pp 291–331 | Cite as

Predator–prey system with strong Allee effect in prey



Global bifurcation analysis of a class of general predator–prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predator) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.


Predator–prey model Allee effect Global bifurcation Limit cycles Heteroclinic loop 

Mathematics Subject Classification (2000)

34C23 34C25 92D25 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinPeople’s Republic of China
  2. 2.Y.Y. Tseng Functional Analysis Research CenterHarbin Normal UniversityHarbinPeople’s Republic of China
  3. 3.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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