WIAS Preprint No. 2009, (2014)

Adaptive behaviour in a predator-prey model leads to multiple equilibrium states


  • Pimenov, Alexander
  • Rachinskii, Dmitrii
  • Korobeinikov, Andrei

2010 Mathematics Subject Classification

  • 92D30 34D20


  • Lotka-Volterra model, predator-prey model, coexistence, stability of biosystems, multiple equilibria, predator pit, fold bifurcation




There is evidence that multiple stable equilibrium states are possible in real-life ecological systems. In order to verify a hypothesis that such a multitude of equilibrium states can be caused by adapting of animal behaviour to changes of environmental conditions, we consider a simple predator-prey model where prey changes a mode of behaviour in response to the pressure of predation. This model exhibits two stable coexisting equilibrium states with basins of attraction separated by a separatrix of a saddle point.

Appeared in

  • Theoret. Population Biol., 101 (2015) pp. 24--30.

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