Geodesic
Dynamics of relay systems with hysteresis and harmonic perturbation
Eurasian mathematical journal, Tome 15 (2024) no. 2, pp. 48-60

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We consider a system of ordinary differential equations with a relay hysteresis and a harmonic perturbation. We propose an approach that allows one to decompose an $n$-dimensional system into one- and two-dimensional subsystems. The approach is illustrated by a numerical example for the system of dimension $3$. As a result of the decomposition, a two-dimensional subsystem with non-trivial Jordan block in right-hand side is studied. For this subsystem we prove a theorem on the existence and uniqueness of an asymptotically stable solution with a period being multiple to period of the perturbation. Moreover, we show how to obtain this solution by tuning the parameters defining the relay. We also provide a supporting example in this regard. 
@article{EMJ_2024_15_2_a3,
     author = {A. M. Kamachkin and D. K. Potapov and V. V. Yevstafyeva},
     title = {Dynamics of relay systems with hysteresis and harmonic perturbation},
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     pages = {48--60},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2024_15_2_a3/}
}
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A. M. Kamachkin; D. K. Potapov; V. V. Yevstafyeva. Dynamics of relay systems with hysteresis and harmonic perturbation. Eurasian mathematical journal, Tome 15 (2024) no. 2, pp. 48-60. http://geodesic.mathdoc.fr/item/EMJ_2024_15_2_a3/