2 results
Search Results
Now showing 1 - 2 of 2
- ItemHomoclinic orbits in a two-patch predator-prey model with Preisach hysteresis operator(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Pimenov, Alexander; Rachinskii, DmitriiSystems 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.
- ItemRobust homoclinic orbits in planar systems with Preisach hysteresis operator(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Pimenov, Alexander; Rachinskii, DmitriiWe 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.