TY - JOUR

T1 - The Existence of a Unique Fixed Point of Mappings Generated by a Multidimensional System with Relay Hysteresis

AU - Kamachkin, A.M.

AU - Yevstafyeva, V.V.

AU - Potapov, D.K.

PY - 2023/9/11

Y1 - 2023/9/11

N2 - Abstract: A multidimensional system of ordinary differential equations with relay hysteresis isconsidered. The system parameters are assumed to be such that there exists a family ofcontinuous operators each of which maps some connected compact set into itself. In this case, theoperator corresponds to a periodic orbit with an even number of switching points in the phasespace of the system. For the operator family, a necessary and sufficient condition for the existenceof a single fixed point is obtained.

AB - Abstract: A multidimensional system of ordinary differential equations with relay hysteresis isconsidered. The system parameters are assumed to be such that there exists a family ofcontinuous operators each of which maps some connected compact set into itself. In this case, theoperator corresponds to a periodic orbit with an even number of switching points in the phasespace of the system. For the operator family, a necessary and sufficient condition for the existenceof a single fixed point is obtained.

UR - https://www.mendeley.com/catalogue/5c215566-6226-3764-8d4a-f8a4d0da8b27/

U2 - 10.1134/s0012266123070121

DO - 10.1134/s0012266123070121

M3 - Article

VL - 59

SP - 998

EP - 1002

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 7

ER -