WIAS Preprint No. 1849, (2013)

Homoclinic orbits in a two-patch predator-prey model with Preisach hysteresis operator


  • Pimenov, Alexander
  • Rachinskii, Dmitrii

2010 Mathematics Subject Classification

  • 47J40 92D25 37L15


  • robust homoclinic orbit, Preisach operator, operator-differential equations, predator-prey model, hysteresis operators, rate-independent systems




Systems of operator-differential equations which hysteresis operators can have unstable equilibrium points with an open basin of attraction. In this paper, a numerical example of a robust homoclinic loop is presented for the first time in a population dynamics model with hysteretic response of prey to variations of predator. A mechanism creating this homoclinic trajectory is discussed.

Appeared in

  • , 139 (2014) pp. 285--298.

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