Robust homoclinic orbits in planar systems with Preisach hysteresis operator

7th International Workshop on MUlti-Rate Processes & HYSteresis; 2nd International Workshop on Hysteresis and Slow-Fast Systems

Pimenov, Alexander^1 ; Rachinskii, Dmitrii^2

Weierstrass Institute, Mohrenstr. 39, Berlin

10117, Germany^1

Department of Mathematical Sciences, University of Texas at Dallas, TX, United States^2

关键词: Generic mechanism;    Homoclinic orbits;    Hysteretic response;    Planar systems;    Population dynamics models;    Preisach hysteresis operators;    Systems of ordinary differential equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/727/1/012012/pdf
DOI  :  10.1088/1742-6596/727/1/012012

来源: IOP

【 摘 要 】

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.