WIAS Preprint No. 1994, (2014)

Robust homoclinic orbits in planar systems with Preisach hysteresis operator



Authors

  • Pimenov, Alexander
  • Rachinskii, Dmitrii

2010 Mathematics Subject Classification

  • 47J40 92D25 37L15

Keywords

  • Robust homoclinic orbit, Operator-differential equations, predator-prey model

Abstract

We construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time. We discuss a generic mechanism that creates robust homoclinic orbits and a method for finding them. An example of a homoclinic orbit in a population dynamics model with hysteretic response of the prey to variations of the predator is studied numerically

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