Nonlinear Dynamics

, Volume 85, Issue 4, pp 2549–2567 | Cite as

Prey cannibalism alters the dynamics of Holling–Tanner-type predator–prey models

  • Aladeen Basheer
  • Emmanuel Quansah
  • Suman Bhowmick
  • Rana D. Parshad
Original Paper
First Online:
Received:
Accepted:

Abstract

Cannibalism, which is the act of killing and consumption of conspecifics, has been considered primarily in the predator, despite strong ecological evidence that it exists among prey. In the current manuscript, we investigate both the ODE and spatially explicit forms of a Holling–Tanner model, with ratio-dependent functional response, and show that cannibalism in the predator provides a stabilizing influence as expected. However, when cannibalism in the prey is considered, we show that it cannot stabilize the unstable interior equilibrium in the ODE case, in certain parameter regime, but can destabilize the stable interior equilibrium, leading to a stable limit cycle or “life boat” mechanism, for prey. We also show that prey cannibalism can lead to pattern forming Turing dynamics, which is an impossibility without it. The effects of a stochastic prey cannibalism rate are also considered.

Keywords

Holling–Tanner model Prey cannibalism Stability Turing instability White noise 

Mathematics Subject Classification

Primary 35B36 37C75 60H35 Secondary 92D25 92D40 
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Notes

Acknowledgments

We would like to acknowledge very helpful conversations with Professor Volker Rudolf, in the Department of Biosciences at Rice University, on various ecological concepts pertaining to prey cannibalism, and subsequent mathematical modeling of such phenomenon.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Aladeen Basheer
    • 1
  • Emmanuel Quansah
    • 1
  • Suman Bhowmick
    • 1
  • Rana D. Parshad
    • 1
  1. 1.Department of MathematicsClarkson UniversityPotsdamUSA

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