Robust homoclinic orbits in planar systems with Preisach hysteresis operator

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Date
2014
Volume
1994
Issue
Journal
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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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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Keywords
Robust homoclinic orbit, Operator-differential equations, predator-prey model
Citation
Pimenov, A., & Rachinskii, D. (2014). Robust homoclinic orbits in planar systems with Preisach hysteresis operator (Vol. 1994). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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