WIAS Preprint No. 2157, (2015)

Memory and adaptive behaviour in population dynamics: Anti-predator behaviour as a case study


  • Pimenov, Alexander
  • Kelly, Thomas C.
  • Korobeinikov, Andrei
  • O'Callaghan, Michael J.
  • Rachinskii, Dmitry

2010 Mathematics Subject Classification

  • 92D25 34C55


  • Bi-stability, Preisach operator, hysteresis, adaptation, predator-prey model, refuge




Memory enables to forecast future on the basis of experience, and thus, in some form, is principally important for the development of flexible adaptive behaviour by animal communities. To model memory, in this paper we use the concept of hysteresis, which mathematically is described by the Preisach operator. As case study, we consider anti-predator adaptation in the classic Lotka-Volterra predator-prey model. Despite its simplicity, the model allows to naturally incorporate essential features of an adaptive system and memory. Our analysis and simulations show that a system with memory can have a continuum of equilibrium states with non-trivial stability properties.

Appeared in

  • J. Math. Biol., (2016) pp. 1--27.

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